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: 
It is generally not legal to fly *into* the Grand Canyon - there is a SFRA (Special Flight Rules Area) over much of the canyon which is designed to keep General Aviation traffic from annoying tourists (and away from the commercial air tour operators). For both GA and commercial tours there are altitude restrictions which keep flights well above the canyon rim.  

([You can download a chart of the Grand Canyon SFRA from the FAA](https://www.faa.gov/air_traffic/flight_info/aeronav/digital_products/vfr/))

Were it legal it probably would not be the safest idea anyway: Inside the canyon there are strong, often unpredictable winds. The conditions would be similar to flying a mountain pass, but with substantially less clearance between your wings and the canyon wall in some places.
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.