  Images of five fields in the Local Group dwarf irregular galaxy NGC 6822
obtained with the {\it Hubble Space Telescope} in the F555W and F814W filters
are presented. Photometry for the stars in these images was extracted using the
Point-Spread-Function fitting program HSTPHOT/MULTIPHOT. The resulting
color-magnitude diagrams reach down to $V\approx26$, a level well below the red
clump, and were used to solve quantitatively for the star formation history of
NGC 6822. Assuming that stars began forming in this galaxy from low-metallicity
gas and that there is little variation in the metallicity at each age, the
distribution of stars along the red giant branch is best fit with star
formation beginning in NGC 6822 12-15 Gyr ago. The best-fitting star formation
histories for the old and intermediate age stars are similar among the five
fields and show a constant or somewhat increasing star formation rate from 15
Gyr ago to the present except for a possible dip in the star formation rate
from 3 to 5 Gyr ago. The main differences among the five fields are in the
higher overall star formation rate per area in the bar fields as well as in the
ratio of the recent star formation rate to the average past rate. These
variations in the recent star formation rate imply that stars formed within the
past 0.6 Gyr are not spatially very well mixed throughout the galaxy.
