  Observations of CH$^+$ are used to trace the physical properties of diffuse
clouds, but this requires an accurate understanding of the underlying CH$^+$
chemistry. Until this work, the most uncertain reaction in that chemistry was
dissociative recombination (DR) of CH$^+$. Using an electron-ion merged-beams
experiment at the Cryogenic Storage Ring, we have determined the DR rate
coefficient of the CH$^+$ electronic, vibrational, and rotational ground state
applicable for different diffuse cloud conditions. Our results reduce the
previously unrecognized order-of-magnitude uncertainty in the CH$^+$ DR rate
coefficient to $\sim \pm 20\%$ and are applicable at all temperatures relevant
to diffuse clouds, ranging from quiescent gas to gas locally heated by
processes such as shocks and turbulence. Based on a simple chemical network, we
find that DR can be an important destruction mechanism at temperatures relevant
to quiescent gas. As the temperature increases locally, DR can continue to be
important up to temperatures of $ \sim 600\,\mathrm{K} $ if there is also a
corresponding increase in the electron fraction of the gas. Our new CH$^+$ DR
rate coefficient data will increase the reliability of future studies of
diffuse cloud physical properties via CH$^+$ abundance observations.
