Point process data arise in a number of application areas including neural coding, genomics, high-frequency finance, and more recently, streaming data. The Hawkes process is a flexible modeling approach for such data that exhibit self-exciting behavior. However, the Hawkes process does not accommodate inhibitory effects also observed in such data. In this paper, we present a nonlinear Hawkes model which accommodates inhibition while guaranteeing positivity of the point process intensity. The positivity preserving property allows a parsimonious representation of the Hawkes impulse response using Laguerre orthogonal polynomials. We develop a fast algorithm to perform maximum likelihood estimation and demonstrate the approach with a simulation and also on some neural data.