We present the first 865 mm continuum image with subarcsecond resolution obtained with the Submillimeter Array. These data resolve the Orion KL region into the hot core, the nearby radio source I, the submillimeter counterpart to the infrared source n (radio source L), and new submillimeter continuum sources. The radio to submillimeter emission from source I can be modeled as either the result of proton-electron free-free emission that is optically thick to similar to100 GHz plus dust emission that accounts for the majority of the submillimeter flux, or H- free-free emission that gives rise to a power-law spectrum with a power-law index of similar to1.6. The latter model would indicate similar physical conditions as found in the inner circumstellar environment of Mira variable stars. Future subarcsecond resolution observations at shorter submillimeter wavelengths should easily discriminate between these two possibilities. The submillimeter continuum emission toward source n can be interpreted in the framework of emission from an accretion disk.