To relieve the peak operating power of the electric grid for an electric bus fast-charging station, this paper proposes to install a stationary energy storage system and introduces an optimization problem for obtaining the optimal sizes of an energy buffer. The charging power demands of the fast-charging station are uncertain due to arrival time of the electric bus and returned state of charge of the onboard energy storage system can be affected by actual traffic conditions, ambient temperature and other factors. The introduced optimization is formulated as a stochastic program, where the power matching equality of the total charging demands of connected electric buses is described as a chance constraint by denoting a satisfaction probability, then a stochastic supremum for the operating power of the electric grid is defined by actual data and the problem finally can be solved by convex programming. A case study for an existing electric bus fast-charging station in Beijing, China was utilized to verify the optimization method. The result shows that the operation capacity cost and electricity cost of the electric grid can be decreased significantly by installing a 325 kWh energy storage system in the case of a 99% satisfaction probability.