  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 sub-Hz laser
is characterized by comparison to a second independent system with similar
fractional frequency stability (1 x 10-15 at 1 s). The laser is further
characterized by resolving a 2 Hz wide, ultranarrow optical clock transition in
ultracold strontium.
