This paper develops a method for obtaining the star formation histories of a mixed, resolved population through the use of color-magnitude diagrams (CMDs). The method provides insight into the local star formation rate, analyzing the observations of the Hipparcos satellite through a comparison with synthetic CMDs computed for different histories with an updated stellar evolution library. Parallax and photometric uncertainties are included explicitly and corrected using the Bayesian Richardson-Lucy algorithm. We first describe our verification studies using artificial data sets. From this sensitivity study, the critical factors determining the success of a recovery for a known star formation rate are a partial knowledge of the IMF and the age-metallicity relation, and sample contamination by clusters and moving groups (special populations whose histories are different than that of the whole sample). Unresolved binaries are less important impediments. We highlight how these limit the method. For the real field sample, complete to Mv < 3.5, we find that the solar neighborhood star formation rate has a characteristic timescale for variation of about 6 Gyr, with a maximum activity close to 3 Gyr ago. The similarity of this finding with column integrated star formation rates may indicate a global origin, possibly a collision with a satellite galaxy. We also discuss applications of this technique to general photometric surveys of other complex systems (e.g. Local Group dwarf galaxies) where the distances are well known. Comment: Accepted for publication in Astronomy and Astrophysics