Coded caching is a recently proposed technique that achieves significant performance gains for cache networks compared to uncoded caching schemes. However, this substantial coding gain is attained at the cost of large delivery delay, which is not tolerable in delay-sensitive applications such as video streaming. In this paper, we identify and investigate the tradeoff between the performance gain of coded caching and the delivery delay. We propose a computationally efficient caching algorithm that provides the gains of coding and respects delay constraints. The proposed algorithm achieves the optimum performance for large delay, but still offers major gains for small delay. These gains are demonstrated in a practical setting with a video-streaming prototype.