  The ultra-faint dwarf galaxy Reticulum II (Ret II) exhibits a unique chemical
evolution history, with 72 +10/-12% of its stars strongly enhanced in r-process
elements. We present deep Hubble Space Telescope photometry of Ret II and
analyze its star formation history. As in other ultra-faint dwarfs, the
color-magnitude diagram is best fit by a model consisting of two bursts of star
formation. If we assume that the bursts were instantaneous, then the older
burst occurred around the epoch of reionization and formed ~80% of the stars in
the galaxy, while the remainder of the stars formed ~3 Gyr later. When the
bursts are allowed to have nonzero durations we obtain slightly better fits.
The best-fitting model in this case consists of two bursts beginning before
reionization, with approximately half the stars formed in a short (100 Myr)
burst and the other half in a more extended period lasting 2.6 Gyr. Considering
the full set of viable star formation history models, we find that 28% of the
stars formed within 500 +/- 200 Myr of the onset of star formation. The
combination of the star formation history and the prevalence of
r-process-enhanced stars demonstrates that the r-process elements in Ret II
must have been synthesized early in its initial star-forming phase. We
therefore constrain the delay time between the formation of the first stars in
Ret II and the r-process nucleosynthesis to be less than 500 Myr. This
measurement rules out an r-process source with a delay time of several Gyr or
more such as GW170817.
