ApproachSP member ZeeJay updated these directions from 2009:
From the intersection of Highway 121 and Highway 40 in the town of Roosevelt in the Uinta Basin, drive west on 200 North (Highway 121). Stay on Highway 121 as it quickly bends to the north. Most junctions are marked with signs, but they are very hard to read in the dark. At mile 9.9, just after the actual mile marker 10 at a stop sign, at the hamlet of Neola go straight towards Uintah Canyon. At mile 16.7 continue straight. At mile 18, turn right to Uintah Canyon. At mile 21.9 turn right. At mile 22.2 turn left just after the bridge. Park at the trailhead at mile 25.6.
Breifly put: From the trailhead (7800 feet elevation), follow the trail north along the Uinta River. After about 3.6 miles, you will reach a junction. You will turn left here, crossing Sheep Bridge and onto the Chain Lakes Trail. Follow the trail, steep in places to the Chain Lakes Basin. Lower Chain Lake is about 9.2 miles from the trailhead and at 10,580 feet elevation. 4th Chain Lake is 1.8 miles beyond and at 10,900 feet elevation. Any of these lakes make a fine campsite.
From 4th Chain Lake, take the trail over Roberts Pass to the Lake Atwood Basin, and then over Trailrider Pass to Painter Basin. You could follow the trail all the way to Anderson Pass, but the shortest way is to climb the SE face of Kings/South Kings directly. There is much boulder-hopping, but no major problems.
This route is about 50 miles round trip and usually takes 4-5 days, sometimes more.
A good pair of boots is needed.