Put oven racks in middle and lower thirds of oven and preheat oven to 450°F.
Toss asparagus with 1 TBSP oil, 1/4 tsp salt and 1/4 tsp pepper in a 15 x 10 inch shallow baking pan. Roast on bottom rack, shaking pan once or twice, until just tender, about 10 minutes.
Meanwhile, pat chicken dry and sprinkle all over with 1/2 tsp salt and remaining 1/4 tsp pepper. Heat remaining 2 TBSP oil in ovenproof skillet (not non-stick) over med-high heat until hot but not smoking, then brown chicken, turning over once, until golden (about 6 minutes total).
Transfer skillet to middle of oven and roast until just cooked through, about 5 minutes.
While chicken roasts, puree tahini, water, lemon juice, sugar, garlic, and remaining 1/2 tsp salt in a blender until smooth, about 1 minute. (Add more water if sauce is too thick).
Serve chicken and asparagus drizzled with some of the sauce and with remaining sauce on the side.