A microcalorimetry technique allowing one to measure the specific heat of bulk single crystals of a mass typically10 &mgr;g, with a relative resolution&Dgr;c/cof10−4is presented. The well known ac steady state technique is employed. The sample holder is a polymer membrane with lithographically patterned thermometer and heaters made out of metallic thin films. The diameter of the useful area is 0.6 mm and the specific heat of the addendum is1.5 &mgr;J/Kat 100 K. The sample is thermally coupled to the membrane through a gold thin film sputtered on its surface. The thermal coupling time constant of the sample is∼5 ms, allowing to work at frequencies of 10 Hz. The method was applied to small single crystals of YBCO, providing the specific heat jump at the superconducting transition with a relative resolution of10−2and a precision of10−1. The method is optimized at the temperature range 40–160 K, but can easily be modified for lower temperatures. ©1997 American Institute of Physics.