  We determine the electronic structure of the one-dimensional spin-1/2
Heisenberg compound $\gamma$-LiV$_2$O$_5$, which has two inequivalent vanadium
ions, V(1) and V(2), via density-functional calculations. We find a relative
V(1)-V(2) charge ordering of roughly $70:30$. We discuss the influence of the
charge ordering on the electronic structure and the magnetic behavior. We give
estimates of the basic hopping matrix elements and compare with the most
studied $\alpha '$-NaV$_2$O$_5$.
