We present a dynamical theory of complex cooperative projects such as large engineering design or software development efforts, comprised of concurrent and interrelated tasks. The model accounts for temporal fluctuations both in task performance and in the interactions between related tasks. We show that as the system size increases, so does the average completion time. Also, for fixed system size, the dynamics of individual project realizations can exhibit large deviations from the average when fluctuations increase past a threshold, causing long delays in completion times. This effect is in agreement with empirical observations, and can be mitigated by arranging projects in a hierarchical or modular structure.