In this letter we describe the ground-state magnetic structure of the highly anisotropic helimagnet Cr$_{1/3}$NbS$_2$ in a magnetic field. A Heisenberg spin model with Dyzaloshinkii-Moriya interactions and magne- tocrystalline anisotropy allows the ground state spin structure to be calculated for magnetic fields of arbitrary strength and direction. Comparison with magnetization measurements shows excellent agreement with the predicted spin structure.