New low-temperature thermochronological data analyses (apatite fission track and apatite and zircon [U-Th]/He) on rocks from the southern (Pacific) margin of Mexico between Acapulco and the western Gulf of Tehuantepec, where pre–middle Eocene arc and forearc complexes are expected but missing, show that this continental margin was subjected to an important Tertiary exhumational event. Exhumation is constrained to ca. 32–20 Ma in the west (Acapulco) and to ca. 19–11 Ma in the east (Puerto Angel) and was thus eastwardly diachronous. The diachroneity is interpreted as relating to the migration of the Chortis block, representing the western end of the Caribbean plate. The amount of exhumation along the trend is constrained to roughly 4–5 km (~0.3–0.6 km/m.y.). These magnitudes and rates are much less than previous estimates of 2.5–4 km/m.y. during the Oligocene, which are likely overestimated. These faster rates have been employed in a competing model for arc removal by orthogonal subduction erosion (i.e., Chortis block not involved), which is accordingly questioned. The exhumation was not due to shearing or fault-related uplift as the Chortis block migrated, but rather to the inception of subduction along Mexico in the wake of Chortis block migration. A four-part history applies to southern Mexico that is eastwardly diachronous: (1) inception of arc magmatism as the Chortis block first moved over the ~150 km depth contour of the Farallon/Cocos Benioff zone; (2) uplift and exhumation of basement as southern Mexico encountered and overrode the site of the Farallon/Cocos Benioff zone; (3) northward migration of arc magmatism as the Chortis block left the cross section and North America continued to advance further onto the Cocos plate, producing flat slab subduction geometry; and (4) resumption of forearc subsidence once the Mexican margin had acquired a subduction zone hanging-wall geometry. The missing arc terrane along southern Mexico is the Chortis block.