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 $Vapprox26$, 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.
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