The Chiral Magnetic Effect (CME) is a macroscopic manifestation of fundamental chiral anomaly in a many-body system of chiral fermions, and emerges as anomalous transport current in the fluid dynamics framework. Experimental observation of CME is of great interest and has been reported in Dirac and Weyl semimetals. Significant efforts have also been made to look for CME in heavy ion collisions. Critically needed for such search, is the theoretical prediction for CME signal. In this paper we

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... rt a first quantitative modeling framework, the Anomalous Viscous Fluid Dynamics (AVFD), which computes the evolution of fermion currents on top of realistic bulk evolution in heavy ion collisions and simultaneously accounts for both anomalous and normal viscous transport effects. The AVFD allows a quantitative understanding of the generation and evolution of CME-induced charge separation during hydrodynamic stage as well as its dependence on theoretical ingredients. With reasonable estimates of key parameters, the AVFD simulations provide the first phenomenologically successful explanation of the measured signal in 200AGeV AuAu collisions.