We demonstrate phase and frequency stabilization of a diode laser at the thermal noise limit of a passive optical cavity. The system is compact and exploits a cavity design that reduces vibration sensitivity. The subhertz laser is characterized by comparison with a second independent system with similar fractional frequency stability (1x10(-15) at 1 s). The laser is further characterized by resolving a 2 Hz wide, ultranarrow optical clock transition in ultracold strontium.