Hi, I'm and INTJ and believe this is the perfect type for chess. I think it necessary to be strongly intuitive and to have a powerful thinking side to play chess. Intuition allows you to make powerful connections during the game, which will lead you to great combination and finished. Moreover I believe an NT is the best sort of chess player. Though Introversion may slightly also benefit a player, whilst J/P will not make any sort of difference.
Myers-Briggs Types and Chess

Isn't "extraverted" just another way of saying "stupid"?
hahaha, I am a big E (>75%) and I came out of university first of my year etc.. so I am not sure that your logic iw watertight. But it is true that I have problems in my club because I make noise, I enjoy the bar and I prefer making friends over winning games :-)
And when I shake hands, I look people in the eyes, kindly.. never at their shoes...
I have always found Myers-Briggs to be an interesting and useful tool.
I am an ENTP. T and F are actually pretty much an even split while I have always scored 100% P.
There are many ways to play and enjoy chess and I think there is something for every personality type.
When I was younger I played a lot of club chess and had some success on the junior circuit for a while. I never liked memorizing openings, studying games or using databases. Instead I studied imbalances and combinations. My opening repetroire consisted of agressive and unusual gambits and other openings which let me use my tactical strengths in the middle game. In some respects, I looked at chess as a battle of wits, wills and creativity -- I often played the person, not the position.
There was definitely a ceiling in terms of how good I could be playing like this but I was perfectly happy with that. I knew what I would have to do to break 1900 but I simply wasn't interested in that aspect of chess.
It is also important that if you know your personality type that you know how to deal with your weaknesses. Chess taught me a lot about myself.. how to pay attention to detail, for example.

I don't trust personality test that involve filling out a little bubble, especially since we really don't know ourselves well enough and just "whatever" through it. I think story pictures like TAT and Rorschach test do better since they're under the radar and more projective. Though there's still controversy over accurate interpretation of results.

No personality tests are perfect. I have drifted from INTP to INFP over the years and am now boarding on ENFP. The N and P have always been very strong and consistent. I think my personality has changed over the years, but I think I am also guilty of over-thinking some of the questions. I went from T to F when I started looking at the questions that drive those elements of the profile differently. I have a very analytic process of making decisions (highly "T" oriented process), but I came to realize that in the end, it was my gut that was driving the decision more than my analysis.
So who knows, probably over thinking it.... Hmmmmmm sounds quite "T" like.. lol
I'm an INTP as well. People actually don't "change between T and F" or other functions; each individual has a very unique personality, their cognitive functions being stronger or weaker depending on genetic, how they are raised, etc etc.
A great forum, this particular article addressing chess and MBTI, can be found here at personality cafe. I've been into and studying MBTI for years, this is a neat place to learn more for the curious.

i am INT then pretty 50-50 on the J-P which flip flips every time i take the test, and is always borderline.

I'm INFP but nearly INTP; It's a close call and I've gotten both results before. Looks like the most common trait here is the N for intuitive, interesting!
Wow, I feel like the only ISTP here. I'm a sort of mix between ISTP and INTP, and personally I'm wondering if S or N is better for chess.

I'm an ENTP. I'm not the loudest person around--but I am around the club! And everyone knows they can distract me by starting up an interesting conversation near me... I have a reputation for unorthodox openings and playing almost purely positional middlegames. Even my "respectable" openings are highly asymmetrical: Reti system, Nimzo, QID... Calculation can't be avoided, but I generally "feel" the squares and the pressure on them, rather than counting, and I put pieces "where they need to be" more than follow specific middlegame plans. My endgame sucks, partially because I focus more on getting a good, complex middlegame than a favorable endgame, and partially because it's BORING. I make speculative material sacrifices to improve my position more often than other players at my level (class B), and am far more likely to sacrifice excess material in a middlegame attack than I am to sit on it through a comfortable endgame. Also, I love analyzing games by discussing possibilities with strong players, and I think I learn a lot more from that than by reading books (which I also do).

INTP here. I thought there would be more INTJ players, maybe because Bobby Fischer has such a big impact on chess perception as a pure INTJ. But I think again and see much chess masters of the past and present as INTP (Kasparov, Karpov, maybe Carlsen). Of course it is all interpretation and we could not know how they really are/were. Here is my take on the results:
Introversion is not essential to be a good chess player, in my opinion, but I think much introvert people are attracted to this type of activity. It is thus understandable to see more introvert players.
Intuition, on the other hand, is quite useful when you struggle to find a good recovery or a suprising attack in a tense position. Sensing would be better when it comes to knowing patterns and perhaps reacting quickly in rapid games. I still feel intuition would be slightly superior in chess but that's my opinion.
As of thinking, it is quite obvious that we should see a majority of chess players with it, althought it doesn't mean you cannot have emotions and play chess.
Perception/Judgement would be the most diverse category regarding chess because good players could be either way. Perceptive players would imagine complex schemes and positions to blow the opponent defense while judging players might have a stronger sense of "correctness" regarding their own pawn structures and development. If you see a player say "you might have played this or that with different results" they are perceptive I think while someone saying "this was a bad move, Xyz is clearly winning here" would be more of a judging player.
INTP, INTJ and perhaps ISTX are the personalities we should expect seing in chess players but, again, it is just another test where the results may easily be far from reality. So nobody should be discouraged by these kind of classifications. If you like to play chess, it is still the strongest indicator that you should play it.

Between my MBTI judgment and my experience playing people I know well enough to type, I would say S helps a lot with memorizing opening lines, with playing endgames, and with utilizing traps and standard tactics. N is better for positional middlegames and strange positions. The TP combination signifies "introverted thinking" (Ti), which is probably best suited to finding the best move, while the TJ combination signifies "extroverted thinking" (Te), which is probably better at spotting potential tactical combinations

ISTP here. Took MBTI / Strong's twice. Was in chess club in school. Now pushing 50 and never get tired of it. I do better when I am not eating and playing chess at the same time. But i hardly have time so play during lunch and supper. Live in the 700 -800s blitzing. I think my functional stack keeps me from taking it too seriously and the tertiary Ni probably doesn't help. I am Ti dominant with auxiliary Se. The introversion probably keeps me coming back for more. I am betting on alot of Ni's here. Sis is an Ni and lots of fun to "take apart and put back together" but I have never been able to "fix" her. She likes chess too but won't play with me. Says I talk too much. ....Please be relevant, helpful & nice!
Interesting, thanks.