  We present the first direct lattice calculation of the isovector sea-quark
parton distributions using the formalism developed recently by one of the
authors. We use $N_f=2+1+1$ HISQ lattice gauge ensembles (generated by MILC
Collaboration) and clover valence fermions with pion mass 310 MeV. We are able
to obtain the qualitative features of the nucleon sea flavor structure even at
this large pion mass: We observe violation of the Gottfried sum rule,
indicating $\overline{d}(x) > \overline{u}(x)$; the helicity distribution obeys
$\Delta \overline{u}(x) > \Delta \overline{d}(x)$, which is consistent with the
STAR data at large and small leptonic pseudorapidity.
