Using approximately 1.3 fb−1 of data collected by the D0 detector between 2002 and 2006, we measure the lifetime of the B±c meson in the B±c→J/ψμ±+X final state. A simultaneous unbinned likelihood fit to the J/ψ+μ invariant mass and lifetime distributions yields a signal of 881±80(stat) candidates and a lifetime measurement of τ(B±c)=0.448+0.038−0.036(stat)±0.032(syst) ps.Received 19 May 2008DOI:https://doi.org/10.1103/PhysRevLett.102.092001©2009 American Physical Society