  Binary neutron stars (BNS) mergers are prime sites for $r$-process
nucleosynthesis. Their rate determines the chemical evolution of heavy elements
in the Milky Way. The merger rate of BNS is a convolution of their birth rate
and the gravitational radiation spiral-in delay time. Using the observed
population of Galactic BNS we show here that the lifetimes of pulsars in
observed BNSs are sufficiently short that the ages of BNSs have little to no
effect on the observed merger time distribution. We find that at late times
($t\gtrsim 1$ Gyr) the gravitational wave delay time distribution (DTD) follows
the expected $ t^{-1}$. However, a significant excess of rapidly merging
systems (between $40-60\%$ of the entire population) is apparent at shorter
times. Although the exact shape of the DTD cannot be determined with the
existing data, in all models that adequately describe the data we find at least
$40\%$ of BNSs with merger times less than 1Gyr. This population of rapid
mergers implies a declining deposition rate of $r$-process materials that is
consistent with several independent observations of heavy element abundances in
the Milky Way. At the same time this population that requires initial binary
separations of roughly one solar radius clearly indicates that these binaries
had common envelope progenitors. Our results suggest that a significant
fraction of future LIGO/Virgo BNS mergers would reside in star forming
galaxies.
