This paper proposes a pricing scheme for the day-ahead market in power systems with a large percentage of renewable stochastic production. To clear the day-ahead market, instead of a simplistic deterministic model, we use a two-stage stochastic programming model that embodies a prognosis of future operating conditions. Non-convexities due to start-up costs and the on/off status of generators and their minimum power outputs are properly taken into account. Our goal is to obtain uniform day-ahead clearing prices that deviate in the least possible manner from marginal prices and that allow producers to recover their costs without uplifts. The proposed methodology is illustrated using a simple example and a realistic case study.