We present constraints on violations of Lorentz invariance based on archival lunar laser-ranging (LLR) data. LLR measures the Earth-Moon separation by timing the round-trip travel of light between the two bodies and is currently accurate to the equivalent of a few centimeters (parts in 10(11) of the total distance). By analyzing this LLR data under the standard-model extension (SME) framework, we derived six observational constraints on dimensionless SME parameters that describe potential Lorentz violation. We found no evidence for Lorentz violation at the 10(-6) to 10(-11) level in these parameters. This work constitutes the first LLR constraints on SME parameters.