Increasingly detailed consumer information makes sophisticated price discrimination possible. At fine levels of aggregation, demand may not obey standard regularity conditions. We propose a new randomized sales mechanism for such environments. Bidders can "buy-it-now" at a posted price, or "take-a-chance" in an auction where the top d > 1 bidders are equally likely to win. The randomized allocation incentivizes high-valuation bidders to buy-it-now. We analyze equilibrium behavior and apply our analysis to advertiser bidding data from Microsoft Advertising Exchange. In counterfactual simulations, our mechanism increases revenue by 4.4% and consumer surplus by 14.5% compared to an optimal second-price auction.