The Hacienda Chichen has a wonderful project with the local community of Ixcalacoop whereby you can spend a week at the hacienda (free, in a "volunteer" cottage on the grounds) if you work each day for a few hours in the community. This usually means teaching English at the local schools. You don't have to be a certified teacher; you just have to know English and be willing to share and spend time with the local children. I have volunteered other places in Mexico and found it very rewarding and a terrific way to blend in and get to know the local Mayan people.
This is also a way to experience Chichen Itza at your own pace, different times of day, and away from the crowds. Just another travel option.