Question: I haven't looked at the Grand Canyon on a sectional yet, but I know that it is definitely big enough (by far) so that someone could fly a plane under the level of the rim and stil meet all of clearance requirements for VFR flight. 

Is it legal, and safe to take an airplane into the canyon?

Answer: 
Safe maybe, but not legal. Not anymore - the helicopter tours did fly into the canyon years ago, but it became illegal in 1987, prompted by a mid-air collision in 1986. [A Special Federal Aviation Regulations (SFAR)](https://www.faa.gov/about/office_org/headquarters_offices/arc/programs/grand_canyon_overflights/documentation/StatutoryRegulatoryandLitigationBackground.pdf) was adopted which regulates traffic below 14,500 ft MSL. This height limit can be raised seasonally to 18.000 ft, and only commercial tour operators are allowed to fly below. For GA traffic three small north-south lanes allow crossing at 10,500 (southbound) rsp. 11,500 ft (northbound). Now even the number of fixed wing and helicopter tour flights is restricted to reduce noise.
December 1979. Air Force F4C, call sign taste 27 got permission from Albuquerque center to fly into the canyon. Was told we were making history, that we were the last jet to be allowed into the canyon.