Background: Monte Carlo (MC) simulations are considered the gold-standard for accuracy in radiotherapy dose calculation; however, general purpose MC engines are computationally demanding and require long runtimes. For this reason, several groups have recently developed fast MC systems dedicated mainly to photon and proton external beam therapy, affording both speed and accuracy. Purpose: To support research and clinical activities at the Heidelberg Ionbeam Therapy Center (HIT) with actively scanned helium ion beams, this work presents MonteRay, the first fast MC dose calculation engine for helium ion therapy. Methods: MonteRay is a CPU MC dose calculation engine written in C++, capable of simulating therapeutic proton and helium ion beams. In this work, development steps taken to include helium ion beams in MonteRay are presented. A detailed description of the newly implemented physics models for helium ions, for example, for multiple coulomb scattering and inelastic nuclear interactions, is provided. MonteRay dose computations of helium ion beams are evaluated using a comprehensive validation dataset, including measurements of spread-out Bragg peaks (SOBPs) with varying penetration depths/field sizes, measurements with an anthropomorphic phantom and FLUKA simulations of a patient plan. Improvement in computational speed is demonstrated in comparison against reference FLUKA simulations.