Put oven racks in middle and lower thirds of oven and preheat oven to 450°F.
Toss asparagus with 1 tablespoon oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a 15- by 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 teaspoon salt and remaining 1/4 teaspoon pepper.
Heat remaining 2 tablespoons oil in a 12-inch heavy ovenproof skillet (not nonstick) over moderately 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, purée tahini, water, lemon juice, sugar, garlic, and remaining 1/2 teaspoon 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 sauce and with remaining sauce on the side.
