  We estimate multiplicative character sums taken on the values of a
non-homogeneous Beatty sequence $\{[\alpha n + \beta] : n =1,2,... \}$, where
$\alpha,\beta\in\R$, and $\alpha$ is irrational. Our bounds are nontrivial over
the same short intervals for which the classical character sum estimates of
Burgess have been established.
