We study the convolutional phase retrieval problem, of recovering an unknown signal <inline-formula> <tex-math notation="LaTeX">$x \in \mathbb C^{n} $ </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> measurements consisting of the magnitude of its cyclic convolution with a given kernel <inline-formula> <tex-math notation="LaTeX">$a \in \mathbb C^{m} $ </tex-math></inline-formula>. This model is motivated by applications such as channel estimation, optics, and underwater acoustic communication, where the signal of interest is acted on by a given channel/filter, and phase information is difficult or impossible to acquire. We show that when <inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> is random and the number of observations <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> is sufficiently large, with high probability <inline-formula> <tex-math notation="LaTeX">$x$ </tex-math></inline-formula> can be efficiently recovered up to a global phase shift using a combination of spectral initialization and generalized gradient descent. The main challenge is coping with dependencies in the measurement operator. We overcome this challenge by using ideas from decoupling theory, suprema of chaos processes and the restricted isometry property of random circulant matrices, and recent analysis of alternating minimization methods.