  We have performed the first global QCD analysis to include the CCFR and NuTeV
dimuon data, which provide direct constraints on the strange and anti-strange
parton distributions, $s(x)$ and $\bar{s}(x)$. To explore the strangeness
sector, we adopt a general parametrization of the non-perturbative $s(x),
\bar{s}(x)$ functions satisfying basic QCD requirements. We find that the
strangeness asymmetry, as represented by the momentum integral $[S^{-}]\equiv
\int_0^1 x [s(x)-\bar{s}(x)] dx$, is sensitive to the dimuon data provided the
theoretical QCD constraints are enforced. We use the Lagrange Multiplier method
to probe the quality of the global fit as a function of $[S^-]$ and find
$-0.001 < [S^-] < 0.004$. Representative parton distribution sets spanning this
range are given. Comparisons with previous work are made.
