The variability of the high-energy gamma ray sources in the Third EGRET catalog is analyzed by a new method. We re-analyze the EGRET data to calculate a likelihood function for the flux of each source in each observation, both for detections and upper limits. These functions can be combined in a uniform manner with a simple model of the flux distribution to characterize the flux variation by a confidence interval for the relative standard deviation of the flux. The main result is a table of these values for almost all the cataloged sources. As expected, the identified pulsars are steady emitters and the blazars are mostly highly variable. The unidentified sources are heterogeneous, with greater variation at higher Galactic latitude. There is an indication that pulsar wind nebulae are associated with variable sources. There is a population of variable sources along the Galactic plane, concentrated in the inner spiral arms.

Accepted by ApJ. 13 pages, 3 figures, 2 tables. Machine-readable copies of Table 1 are at http://giants.stanford.edu/~pln/vartbl1/