Chichen Itza is possible to get on Deity with Liberty finisher GE. Notre Dame, to me, is in the same boat as the GL. I actually got the GL once on Deity, but I have never built Notre Dame ever in my life. Chichen Itza is also possible because Civil Service requires Writing, but Physics takes the same number of techs without Writing. I simply don't know who can get there in time. Babylon with Writing detour? The Maya?
Well yes I suppose it is possible to get Chichen Itza but I think the odds run pretty heavily against you. Actually I'm not really sure what is so great about Chichen Itza anyway - +50% golden ages is nice but I never get that many early golden ages to really make that much of a difference. If you have that much happiness to get these frequently then your population is probably too low.