Why do I keep getting this message on my Chimp tablet? "Unfortunately the process com.google.process.gapps has stopped"

Here's something you can try to resolve the problem:

http://forums.androidcentral.com/t-galaxy-s-iii/189798-unfortunately-process-com-google-process-gapps-has-stopped-20.html

I would try clearing the data and cache on Google Play services
and on Google Play Store first as it's the usual culprit. Keep in mind that after a reboot, Google Play Services will have to rebuild the data and cache and it will need a WiFi connection to do it. Launch the Play Store to get the ball rolling. If it seems balky for a minute or two don't stress as it's just rebuilding the cache. If it asks you to log in again with your Google account don't be concerned as that is part of the rebuild.