The muon decay parameter has been measured by the TWIST collaboration. We find = 0.74964 0.00066)(stat.) 0.00112(syst.), consistent with the standard model value of 3/4. This result implies that the product P of the muon polarization in pion decay, P , and the muon decay parameter falls within the 90% confidence interval 0.9960 < P < 1.0040. It also has implications for left-right-symmetric and other extensions of the standard model. 2005 The American Physical Society.