Because quantum chromodynamics (QCD) is non-perturbative at low energies, strong in- teractions at the ∼ GeV scale are very challenging to understand. Theoretical progress has been made recently using QCD-based effective field theories (EFT). The short-distance physics of the effective theory is absorbed into a limited number of low energy constants (LECs), which are determined by direct experimental measurement. The MuSun experi- ment is measuring the rate Λd for muon capture on the deuteron, which is the simplest weak interaction in a two nucleon system. Λd will be used, in turn, to better determine a funda- mental LEC known as dR in the EFT. An improvement in the precision of this LEC will improve our understanding of several other processes in the two-nucleon sector: pp fusion, the main source of energy in the sun and other main-sequence stars and neutrino-deuteron scattering, as observed in the SNO experiment. The MuSun experiment determines Λd via a precision measurement of the negative muon lifetime in deuterium. The time difference between an incoming muon, which stops in deuterium, and the subsequent decay electron characterizes the muon disappearance rate. That disappearance rate is the sum of the ordinary muon decay rate and the nuclear capture rate. The ultimate goal of the MuSun experiment is to determine the nuclear capture rate (Λd) to a precision of 1.5 %, an order of magnitude improvement over previous efforts. The principal experimental development required to achieve this goal is a cryogenic (T ∼30K) time projection chamber, which not only serves as the deuterium gas target, but also provides an unambiguous measurement of muon stopping position - muons that stop in high Z materials outside the fiducial deuterium volume produce a very large systematic error. The low temperature helps minimize several other systematic errors. The MuSun experiment is taking place at the Paul Scherrer Institut in Villigen, Switzer- land. Over the past 5 years, the MuSun collaboration has staged 4 major experimental production runs. In this thesis, I present a measurement of the muon capture rate on deu- terium, as determined from data taken in the summer of 2013. The estimated statistical and systematic error is about 7.5%.