This is exactly my problem.
Facebook Email Setup - Password?
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And mine 
What if I close my facebook account? And, where do you send the PGN files?
Mar 20, 2014
0
#4
@matematikisto- Please send me a message with the email address that you'd like to be added to your account (don't post it here). Thank you!
Oh wow. I've posted questions twice in the forums and got no response from any staff.
Maybe next time I should have a woman post them so someone will respond.
In my experience, it seems that the forums are largely a 'self-service' help feature. For issues like the password problem, you need to actually contact the Tech Support people directly.
https://support.chess.com/customer/portal/emails/new
Same problem
Apr 30, 2015
0
#12
As a Chess.com member who logs in with Facebook, you can set up a Chess.com password by going to your account settings > change password:
https://www.chess.com/home/change_password
Once you have your password set up, then you can use that to set up your email address. When we built that feature a few years ago, I was sure we had a link to guide you to setting up a password first.
But I can't change my password, because i dont know what it is currently.
It's not my facebook password.
Apr 30, 2015
0
#14
Can you send me a direct message on site with the email address you'd like associated with your account @TimRoberts1? Don't post it here :)
Once I have that, I can issue you a temporary password and send you a password reset form.
bur seriously, this is a common issue, so it makes no sense to require the assistance of STAFF members. if there is any, what is the default password?
same problem here, and im really considering to upgrade my membership but i need to configure email account, somebody help me please!
Jan 23, 2016
0
#17
I have the same problem... can staff pls set up a password for me, as I log in over facebook but want to change setting, which requires a password i dont have.
And for me, please 
Jan 16, 2018
0
#19
I figured it out! Since you don't have a password, leave the current password field empty.
Trying to set up an email address with my account. I usually log in using Facebook authentication.
When trying to set up an email for my account to enable notifications, it prompts me for a password. It doesn't seem to be accepting my FB password, and I don't recall setting up another one. What am I missing?