Eukaryotic cells are capable of detecting small chemical gradients for a wide range of background concentrations. Ultimately, fluctuations place a limit on gradient sensing and recent work has focused on the role of stochastic receptor occupancy as one possible limiting factor. Here, we use a phenomenological approach to add spontaneous motility fluctuations to receptor noise and predict the directional statistics of eukaryotic chemotaxis. Specifically, an Itô diffusion equation with direction-dependent multiplicative noise is developed and analytically studied. We show that our approach can naturally accommodate recent experimental data for the chemotaxis of the social amoeba Dictyostelium.