In this paper, we give a complete classification of Ricci-Bourguignon soliton on real hypersurfaces in the complex hyperbolic space DOUBLE-STRUCK CAPITAL CHn = SU1,n/S(U1Un). Next, as an application, we give a complete classification of gradient Ricci-Bourguignon soliton on Hopf real hypersurfaces in the complex hyperbolic space DOUBLE-STRUCK CAPITAL CHn.