We construct chiral analogues of differential operators acting on classical invariant rings as global sections of sheaves of chiral differential operators (CDO) associated with vector bundles on smooth open subvarieties of affine GIT quotients, using BRST reduction. As an application, we construct new infinite families of simple conformal quasi-lisse vertex algebras. Inparticular, we show that the CDO algebra on the base affine space G/U of type A is quasi-lisse and we extend the Gelfand-Graev action (a mysterious Weyl group action on the ring of differential operators on G/U) to the CDO algebra on G/U. This is a joint work in progress with Tomoyuki Arakawa and Xuanzhong Dai.