We report on the first in a series of studies of the Carina dwarf spheroidal galaxy , a nearby satellite of our Galaxy . Our two major results are : 1 ) precise BI photometry ( \sigma _ { B - I } \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 0.05 for V \lower 2.15 pt \hbox { $ \buildrel < \over { \sim } $ } 22 ) for 11,489 stars in the Carina field , and 2 ) the detection of two , morphologically distinct , horizontal branches in Carina , which confirms that star formation occurred in two well-separated episodes . The old horizontal branch and RR Lyrae instability strip belong to a \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 Gyr stellar population , while the populous red-clump horizontal branch belongs , presumably , to a \sim 6 Gyr stellar population . We derive a distance modulus ( m - M ) _ { 0 } = 20.09 \pm 0.06 for Carina from the apparent magnitudes of the old horizontal branch and the tip of the red giant branch ( RGB ) , and discuss modifications to the previously estimated distance , total magnitude , and stellar ages of Carina . Using the color of the RGB , we estimate the metallicities of the younger and older populations to be { [ Fe / H ] } \simeq - 2.0 and –2.2 , respectively .