In real-time listening enhancement applications, such as hearing aid signal processing, sounds must be processed with no more than a few milliseconds of delay to sound natural to the listener. Listening devices can achieve better performance with lower delay by using microphone arrays to filter acoustic signals in both space and time. Here, we analyze the tradeoff between delay and squared-error performance of causal multichannel Wiener filters for microphone array noise reduction. We compute exact expressions for the delay-error curves in two special cases and present experimental results from real-world microphone array recordings. We find that delay-performance characteristics are determined by both the spatial and temporal correlation structures of the signals.