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This paper presents Timed Quorum System (TQS), a quorum system for large-scale and dynamic systems. TQS provides guarantees that two quorums, accessed at instances of time that are close together, intersect with high probability. We present an algorithm that implements TQS at its core and that provides operations that respect atomicity with high probability. This TQS implementation has quorums of size O(√nD) and expected access time of O(log √nD) message delays, where n measures the size of the system and D is a required parameter to handle dynamism. This algorithm is shown to have complexity sublinear in size and dynamism of the system, and hence to be scalable. It is also shown that for systems where operations are frequent enough, the system achieves the lower bound on quorum size for probabilistic quorums in static systems, and it is thus optimal in that sense.