We have used the Mid-InfraRed Instrument (MIRI) on the James Webb Space Telescope (JWST) to obtain the first spatially resolved, mid-infrared images of IIZw096, a merging luminous infrared galaxy (LIRG) at z = 0.036. Previous observations with the Spitzer Space Telescope suggested that the vast majority of the total IR luminosity (L
IR) of the system originated from a small region outside of the two merging nuclei. New observations with JWST/MIRI now allow an accurate measurement of the location and luminosity density of the source that is responsible for the bulk of the IR emission. We estimate that 40%–70% of the IR bolometric luminosity, or 3–5 × 1011
L
⊙, arises from a source no larger than 175 pc in radius, suggesting a luminosity density of at least 3–5 × 1012
L
⊙ kpc−2. In addition, we detect 11 other star-forming sources, five of which were previously unknown. The MIRI F1500W/F560W colors of most of these sources, including the source responsible for the bulk of the far-IR emission, are much redder than the nuclei of local LIRGs. These observations reveal the power of JWST to disentangle the complex regions at the hearts of merging, dusty galaxies.