High-precision, high-cadence radial velocity monitoring over the past 8yr at the W. M. Keck Observatory reveals evidence for a third planet orbiting the nearby (4.69pc) dM4 star GJ 876. The residuals of three-body Newtonian fits, which include GJ 876 and Jupiter-mass companions b and c, show significant power at a periodicity of 1.9379days. Self-consistently fitting the radial velocity data with a model that includes an additional body with this period significantly improves the quality of the fit.