Its been over ten years since I was on Chinchorro but I still try and keep up with the diving there. Last time I was in Ixcalak (four months ago) I was told that there were just a few operators that had permits to dive there. http://www.xtcdivecenter.com/
is one of the few operators who do have permits. It seems the Mexican goverment has zoned Chinchorro into various usage areas so diving is restricted to certain areas of the atoll which is quite large (imagine Cozumel underwater)
As to the diving, my observations are a bit dated but I guess better than nothing. Reefs were great though the viz where most of the diving was done (lee side) was so so 60 to 80 feet. The outside of the atoll system had great viz but you could hardly ever dive there and I think its now off limits. Marine life, not much pelagics, turtle nurse shark etc. Lots of wrecks though they are mainly on the windward side and I imagine many are off limits now.