Point process data are commonly observed in fields like healthcare and social science. Designing predictive models for such event streams is an under-explored problem, due to often scarce training data. In this work we propose a multitask point process model, leveraging information from all tasks via a hierarchical Gaussian process (GP). Nonparametric learning functions implemented by a GP, which map from past events to future rates, allow analysis of flexible arrival patterns. To facilitate efficient inference, we propose a sparse construction for this hierarchical model, and derive a variational Bayes method for learning and inference. Experimental results are shown on both synthetic data and an application on real electronic health records.