The combustion mechanism in a Compression Ignition Homogeneous Charge (CIHC) engine was studied. Previous experiments done on a four-stroke CIHC engine were modeled using the KIVA-II code with modifications to the combustion, heat transfer, and crevice flow submodels. A laminar and turbulence characteristic time combustion model that has been used for spark-ignited engine studies was extended to allow predictions of ignition. The rate of conversion from one chemical species to another is modeled using a characteristic time which is the sum of a laminar (high temperature) chemistry time, an ignition (low temperature) chemistry time, and a turbulence mixing time. The ignition characteristic time was modeled using data from elementary initiation reactions and has the Arrhenius form. It was found to be possible to match all engine test cases reasonably well with one set of combustion model constants. Combustion was found to be controlled by chemical kinetic rates up to the time of ignition. After ignition, comparisons between the measured cylinder pressure data and predicted pressures showed that good levels of agreement were not possible unless the turbulent mixing time scale was included in the combustion model. This important result implies that turbulent mixing, flame stretch and partial extinction phenomena control the rate of combustion after ignition, even in this engine that is characterized by homogeneous mixtures and the absence of a propagating flame. Ignition is controlled at low temperatures by the ignition timescale. The high temperature laminar chemistry timescale never plays a role in determining the combustion rate since it is generally smaller than the other characteristic times. The combustion regime is classified as being between reaction sheet and distributed reaction combustion.