But it will let you remove it partially?
how do I delete my profile photo?

I would like mine removed as well.
All you have to do is change the photo in your settings. https://www.chess.com/settings/profile
Surely most of you have enough computer mojo to figure that one out.
(Hint: copy somebody else's default picture.)

It doesn't show me how to delete pictures on my profile.
On the website, when you go into your profile settings, there is an X on the upper-right of the current avatar, if it's not the default. Just click the X.
If you mean in the bio/info, you just click it to select and hit backspace or delete on your keyboard.

Hello. Perhaps you should not delete your profile photo, but replace it with a more visually appealing one. Try to find a really nice high quality image on https://blog.depositphotos.com/inspiration-swiss-style-poster-design.html and upload it as your avatar. I agree, sometimes it is indeed very difficult to find visually attractive material. But thanks to services such as Depositphotos this is much easier to do.

It's a good question, but it seems a bit trivial to me, because there are a lot of articles on how to delete a profile photo, or the same avatar and put up a photo you like. Personally, I like to always put a photo that I have in my gallery on my avatar, but even recently I have been doing something different, I ask Depositphotos to remove the background and enjoy the quality of the work, the photo remains as picturesque as ever, and the background imperfections disappear.
It only allows me to change it to another photo,
doesn't have a choice to remove it completely.
What is wrong ?