Small-scale battery energy storage systems (BESS), especially for behind-the-meter applications, are still relatively expensive, but we show that it can be a potent solution to render homes resilient to storm related power outages. We present a stochastic programming model formulation to optimize PV/BESS explicitly accounting for resilience benefits these investments entail, over and above their ability to reduce cost of supply. The stochastic optimization considers uncertainties around storm related grid supply failures as well as variability of solar PV. The model includes an embedded Monte Carlo simulation module that considers storm related outage risks using climate model reanalysis data. It is a least-cost planning framework that optimizes selection of BESS, solar PV, grid supply, and diesel generator, from a homeowner's perspective. We present two case studies with low and high storm risks that demonstrate how different risk exposures can impact on the selection of alternative options to build resilience. Duals, or shadow prices, of demand-supply constraints from the model for both normal days and for storm related contingencies, provide interesting insights into the marginal cost of supply that can inform innovative pricing schemes to promote customer level resilience measures. The case study results reveal significant merits of BESS, in combination with PV, to enhance resilience. We find that in low-risk areas like Bethesda, MD, incremental PV and BESS required for a more resilient system can add $79 (4%) to expected annual electricity costs for a typical household, and a considerably higher $208 (10.6%) in Miami, FL which is at a much greater risk. These options are, however, 27% (in Bethesda) and 20% (in Florida) less expensive than the conventional solution of installing a diesel generator. These results provide insights into the value of BESS as part of a resilient and clean energy solution for households.