The current global chassis control (GCC) frequently makes use of decoupled control methods which depend on driving condition partition and simple rule-based vertical force distribution, and are insufficient to obtain optimal vehicle dynamics performance. Therefore, a novel hierarchical global chassis control system for a distributed electric vehicle (DEV), which is equipped with four wheel driving/steering and active suspension systems, is developed in this paper. The control system consists of three layers: in the upper layer, the desired forces/moments based on vehicular driving demands are determined; in the middle layer, a coordinated control method of longitudinal/lateral/vertical tire forces are proposed; in the lower layer, the driving/steering/suspension control is conducted to realize each distributed tire force. As the most outstanding contribution of this paper, a non-convex optimization problem with multiple constraints for coordinated control of longitudinal/lateral/vertical tire forces is solved, in which (1) tire force distribution problem is theoretically concluded as a constrained non-convex optimization problem, (2) a unique objective function that combines the tire workload and the dynamic ratio of the vertical forces is designed to evaluate tire force distribution, (3) 14 constraints including vehicular driving demands, tire friction limitations and actuator natures are involved to bound each tire force reasonably, and (4) an algorithm that combines constrained optimization and feasible region planning is proposed to solve the constrained non-convex optimization problem. Simulation results based on Matlab/Simulink and CarSim show that the proposed hierarchical global chassis control system effectively achieves better vehicle attitude and handling stability during the accelerated double lane change scenario compared with the other GCC methods.