During its year-long outburst in 1975–76, the transient source A0620–00 reached an intensity of 50 Crab, an all-time record for any X-ray binary. The source has been quiescent since then. We have recently determined accurate values for the black hole (BH) mass, orbital inclination angle, and distance. Building on these results, we have measured the radius of the inner edge of the accretion disk around the BH primary by fitting its thermal continuum spectrum to our version of the relativistic Novikov–Thorne thin-disk model. We have thereby estimated the spin of the BH. Although our spin estimate depends on a single high-quality spectrum, which was obtained in 1975 by OSO-8, we are confident of our result because of the consistent values of the inner-disk radius that we have obtained for hundreds of observations of other sources: H1743-322, XTE J1550-564, and notably LMC X-3. We have determined the dimensionless spin parameter of the BH to be a∗ = 0.12 ± 0.19, with a∗ −0.59 at the 3σ level of confidence. This result takes into account all sources of observational and model-parameter uncertainties. Despite the low spin, the intensity and properties of the radio counterpart, both in outburst and quiescence, attest to the presence of a strong jet. If jets are driven by BH spin, then current models indicate that jet power should be a steeply increasing function of a∗. Consequently, the low spin of A0620–00 suggests that its jet may be disk driven.Astronom