The Baksan Experiment on Sterile Transitions (BEST) was designed to investigate the deficit of electron neutrinos ν_{e} observed in previous gallium-based radiochemical measurements with high-intensity neutrino sources, commonly referred to as the "gallium anomaly," which could be interpreted as evidence for oscillations between ν_{e} and sterile neutrino (ν_{s}) states. A 3.414-MCi ^{51}Cr ν_{e} source was placed at the center of two nested Ga volumes and measurements were made of the production of ^{71}Ge through the charged current reaction, ^{71}Ga(ν_{e},e^{-})^{71}Ge, at two average distances. The measured production rates for the inner and the outer targets, respectively, are [54.9_{-2.4}^{+2.5}(stat)±1.4(syst)] and [55.6_{-2.6}^{+2.7}(stat)±1.4(syst)] atoms of ^{71}Ge/d. The ratio (R) of the measured rate of ^{71}Ge production at each distance to the expected rate from the known cross section and experimental efficiencies are R_{in}=0.79±0.05 and R_{out}=0.77±0.05. The ratio of the outer to the inner result is 0.97±0.07, which is consistent with unity within uncertainty. The rates at each distance were found to be similar, but 20%-24% lower than expected, thus reaffirming the anomaly. These results are consistent with ν_{e}→ν_{s} oscillations with a relatively large Δm^{2} (>0.5  eV^{2}) and mixing sin^{2}2θ (≈0.4).