We present the detection of the reactive ion CO+ toward the prototypical starburst galaxy M82. This is the first secure detection of this short-lived ion in an external galaxy. Values of [CO+]/[HCO+] > 0.04 are measured across the inner 650 pc of the nuclear disk of M82. Such high values of [CO+]/[HCO+] have previously only been measured toward the atomic peak in the reflection nebula NGC 7023. This detection corroborates the scenario in which the molecular gas reservoir in the M82 disk is heavily affected by the UV radiation from recently formed stars. Comparing the column densities measured in M82 with those found in prototypical Galactic photon-dominated regions (PDRs), we need ∼20 clouds along the line of sight to explain our observations. We have completed our model of the molecular gas chemistry in the M82 nucleus. Our PDR chemical model successfully explains the [CO+]/[HCO+] ratios measured in the M82 nucleus but fails by an order of magnitude to explain the large measured CO+ column densities [∼(1–4) x 10↑13 cm↑-2 ]. We explore possible routes to reconcile the chemical model and the observations.