We have searched for time variability of the stars in the central parsec of the Galaxy through K-band (2.2um) imaging and photometry. The observations were made with an array-based camera at the NASA Infrared Telescope Facility in 1991, 1992, and 1993. In 1991, on timescales ranging from 20 seconds to a week, no time variability greater than 0.1 mag was found for about five dozen sources in this region, and the brighter sources were stable to 0.05 mag. On timescales of one to two years, we found a new source near IRS10E that varied in brightness by at least one magnitude and detected variability of 0.15 to 0.5 mag in several other sources, most notably the red giants IRS9 and IRS12N. None of the luminous blue stars identified in the Galactic center region show evidence for variability.