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Detecting data races in shared-memory parallel programs is an important debugging problem. This paper presents a new protocol for run-time detection of data races in executions of shared-memory programs with nested fork-join parallelism and no other inter-thread synchronization. This protocol has significantly smaller worst-case run-time overhead than previous techniques. The worst-case space required by our protocol when monitoring an execution of a program P is O(VN), where V is the number of shared variables in P, and N is the maximum dynamic nesting of parallel constructs in P's execution. The worst-case time required to perform any monitoring operation is O(N). We formally prove that our new protocol always reports a nonempty subset of the data races in a monitored program execution and describe how this property leads to an effective debugging strategy.