If you don't mind a steep and potentially hot hike, you can also get to Chaol Falls overland from Route 98 southeast of Page. It's about 7 miles round trip. You would need a permit from the Navajo Nation. I've done it three times as a dayhike and once as the start of a backpack, all before 2000. When I went, it was on trail all the way, but if you had to be used to following fairly faint trails. On the topo map, the first side canyon of Navajo Canyon downstream of Chaol Canyon is called Butterfly Canyon. There is a jeep road that leaves Hwy 98 and runs northeast on top of the first ridge east of Butterfly Canyon. Where the road peters out, at or before point 5102, drop down a steep hill and continue northeast near the top of the ridge until near point 4926. From there, the trail bends to the east and drops steeply, with switchbacks, down to Chaol Canyon. The falls, called "Pinon Falls" on the topo, are a little bit upstream.
You can walk upstream in the narrowing Chaol Canyon above the Falls, but that will lead into an area the Tribe has closed to passage because of abuse by canyoneers many years ago.
You can also walk downstream, at current water levels, to where Chaol Canyon meets Navajo Creek. I went that way once many years ago in a walk from Page to Rainbow Bridge. (Hwy 98 to Chaol Falls to Navajo Creek to Jayi Canyon to Aztec Creek to Cliff Canyon to Redbud Pass to Redbud Creek to Bridge Creek, for those who are interested; details on demand)