We present the star formation history (SFH) of the faintest known star-forming galaxy, Leo T, based on deep imaging taken with the Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC2). The HST/WFPC2 color-magnitude diagram (CMD) of Leo T is exquisitely deep, extending ~2 mag below the oldest main-sequence turnoff, permitting excellent constraints on star formation at all ages. We use a maximum likelihood CMD fitting technique to measure the SFH of Leo T assuming three different sets of stellar evolution models: Padova (solar-scaled metallicity) and BaSTI (both solar-scaled and α-enhanced metallicities). The resulting SFHs are remarkably consistent at all ages, indicating that our derived SFH is robust to the choice of stellar evolution model. From the lifetime SFH of Leo T, we find that 50% of the total stellar mass formed prior to z ~ 1 (7.6 Gyr ago). Subsequent to this epoch, the SFH of Leo T is roughly constant until the most recent ~25 Myr, where the SFH shows an abrupt drop. This decrease could be due to a cessation of star formation or stellar initial mass function sampling effects, but we are unable to distinguish between the two scenarios. Overall, our measured SFH is consistent with previously derived SFHs of Leo T. However, the HST-based solution provides improved age resolution and reduced uncertainties at all epochs. The SFH, baryonic gas fraction, and location of Leo T are unlike any of the other recently discovered faint dwarf galaxies in the Local Group, and instead bear strong resemblance to gas-rich dwarf galaxies (irregular or transition), suggesting that gas-rich dwarf galaxies may share common modes of star formation over a large range of stellar mass (~10⁵-10⁹ M ☉).