We consider Chern-Simons theory defined on a 3d ball with generalized chiral boundary conditions. While classically this class of boundary conditions leaves the theory conformally invariant, on the quantum level, the theory develops a Weyl anomaly. We will present a natural SL(2,C)-invariant propagator which we will use to compute the anomaly and the associated RG flow perturbatively up to 1-loop. We find that the RG flow is driven by the generalized Ricci tensor. If time permits, we will also comment on the RG flow of generalized chiral boundary conditions in the Courant sigma model. This talk is based on joint work with Pavol Severa and Jan Pulman.