This paper examines the problem of optimizing the charge trajectory of a plug-in hybrid electric vehicle (PHEV), defined as the timing and rate with which the PHEV obtains electricity from the power grid. Two objectives are considered in this optimization. First, we minimize the total cost of fuel and electricity consumed by the PHEV over a 24-hour naturalistic drive cycle. We predict this cost using a previously-developed stochastic optimal PHEV power management strategy. Second, we also minimize total battery health degradation over the course of the 24-hour cycle. This degradation is predicted using an electrochemistry-based model of anode-side resistive film formation in Li-ion batteries. The paper shows that these two objectives are conflicting, and trades them off using a non-dominated sort genetic algorithm, NSGA-II. As a result, a Pareto front of optimal PHEV charge trajectories is obtained. The effects of electricity price and trip schedule on the Pareto front are analyzed and discussed.