The skyline query, aiming at identifying a set of skyline tuples that are not dominated by any other tuple, is particularly useful for multicriteria data analysis and decision making. For uncertain databases, a probabilistic skyline query, called P-Skyline, has been developed to return skyline tuples by specifying a probability threshold. However, the answer obtained via a P-Skyline query usually includes skyline tuples undesirably dominating each other when a small threshold is specified; or it may contain much fewer skyline tuples if a larger threshold is employed. To address this concern, we propose a new uncertain skyline query, called U-Skyline query, in this paper. Instead of setting a probabilistic threshold to qualify each skyline tuple independently, the U-Skyline query searches for a set of tuples that has the highest probability (aggregated from all possible scenarios) as the skyline answer. In order to answer U-Skyline queries efficiently, we propose a number of optimization techniques for query processing, including 1) computational simplification of U-Skyline probability, 2) pruning of unqualified candidate skylines and early termination of query processing, 3) reduction of the input data set, and 4) partition and conquest of the reduced data set. We perform a comprehensive performance evaluation on our algorithm and an alternative approach that formulates the U-Skyline processing problem by integer programming. Experimental results demonstrate that our algorithm is 10-100 times faster than using CPLEX, a parallel integer programming solver, to answer the U-Skyline query.