We present a new measurement of the difference between the nucleon strange and antistrange quark distributions from dimuon events recorded by the NuTeV experiment at Fermilab. This analysis is the first to use a complete next to leading order QCD description of charm production from neutrino scattering. Dimuon events in neutrino deep inelastic scattering allow direct and independent study of the strange and antistrange content of the nucleon. We find a positive strange asymmetry with a significance of 1.6sigma. We also report a new measurement of the charm mass.