  We investigate chiral superconductivity which occurs in the electronic
nematic state. A vortex state in a $c$-axis magnetic field is studied on the
basis of the two-component Ginzburg-Landau model for nematic-chiral
superconductors. It is shown that various vortex lattice structures are
stabilized by nontrivial cooperation of nematicity and chirality in
superconductors. In particular, the vortex lattice structural transition occurs
when a square anisotropy parameter $\nu$ is positive (negative) and the
nematicity is induced along the [110] axis ([100] axis). We discuss
nematic-chiral superconductivity in URu$_2$Si$_2$, Sr$_2$RuO$_4$, and UPt$_3$.
An experimental test for the examination of nematic order and chiral
superconductivity is proposed.
