We fabricate high-Q arsenic triselenide glass microspheres through a three-step resistive heating process. We demonstrate quality factors greater than 2 x 10(6) at 1550 nm and achieve efficient coupling via a novel scheme utilizing index-engineered unclad silicon nanowires. We find that at powers above 1 mW the microspheres exhibit high thermal instability, which limits their application for resonator-enhanced nonlinear optical processes.