My kid is better than me, help!

There is a section of coaches on here, think its great that your supporting their passions. All the money an time my parents put in towards my hockey growing up made alot of fun memories. Tournaments, hotels etc. As long as their having fun !

How long has your son been playing chess? Has he played in any OTB tournaments? Has he reached a plateau and seems stuck without further guidance? 
I ask these questions because it might be just a little early for a coach. (I know I'll get slammed for that, but that's OK).
Here on chess.com there are thousands of tactical puzzles, hundreds of lessons, hundreds of videos (for diamond members), practically endless play at all different time controls, and hundreds of drills for honing ones skills. He might want to avail himself of some of this treasure trove of material before getting a coach. 
However, if he's serious and shows a lot of potential, a good coach can shave years off of the training it takes to get good simply by focusing in on what he needs based on his performance.

Here is a link that will help you find material to get better. They may be more on the old side but they have great value and are free. Also, check out @BlakeyBChess on chess.com or his website ChessPathways.com to start some lessons. He offers a great deal that should benefit you

#1

"not sure how to find a coach for his level"
++ A coach is not necessary. You can coach him yourself. The main point is telling him what not to do: no blitz, no bullet, no opening theory, no play against weak players and what to do: blunder checking, tactics training, analysis of lost games, analysis of master games, endgame study. A book by a top grandmaster costs less and brings more than a mediocre coach.

"How can I support him?
++ You can buy him a pair of good chess books authored by top grandmasters. E.g. "Fundamental Chess Endings" by Karsten Müller or "My Great Predecessors" by Kasparov.

"I work at a university with a great chess team, is it appropriate to reach out?"
++ Joining a chess club is a good idea. Just take care he avoids playing weaker players. That will make him cocky and halt any progress.

Improving Your Chess - Resources for Beginners and Beyond...

https://www.chess.com/blog/RussBell/improving-your-chess-resources-for-beginners-and-beyond

https://www.chess.com/blog/RussBell

I was actually at chess kid and now I am in chess.com

Your son can learn better without coaching from you. Buy him Fritz 17. Don't introduce chess videos. Unless your son is a slow learner.

Kids are really good at pickup up things easily. They are like little sponges 

Absolutely! In fact, I highly recommend you seek information from them rather than us.

Tell them exactly what you told us, that your child is 11 years old, he can beat you at chess, and you are looking for the next step, which is getting coached. They'll take it from there. 

And don't take the first offer you get, just because they offer it. See if they have experience with teaching age 11 children. 

if you think he's that good, and he enjoys playing chess, you should get him a coach methinks

although using yourself as a reference point when saying he's better than you still leaves a lot of information missing because you only have played one game so

Great work! Congratulations for starting them young!

Take your son to weekend OTB tournaments. If he like the Competition. he can join a local chess club. The chess club is vital.in chess Improvement.

The free courses on Chessable have helped me ... and I need the help! "Smithy's Opening Fundamentals" is a free one and has improved my play.  

Hi! My name is Lauren Goodkind and I'm a chess coach and chess author based in California.  I'm available to teach your son chess.  I have been teaching chess to kids and adults for the last 9 years.  

My website is www.ChessByLauren.com

Kids are supposed to beat their parents surely?

Don't worry adout it just keep do practice and then one day you well be best in chess.... Believe me

*doing