We present the detection of the reactive ion CO ^ { + } towards the prototypical starburst galaxy M 82 . 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 M 82 . Such high values of the [ CO ^ { + } ] / [ HCO ^ { + } ] ratio had only been previously measured towards the atomic peak in the reflection nebula NGC 7023 . This detection corroborates that the molecular gas reservoir in the M 82 disk is heavily affected by the UV radiation from the recently formed stars . Comparing the column densities measured in M 82 with those found in prototypical Galactic photon-dominated regions ( PDRs ) , we need \sim 20 clouds along the line of sight to explain our observations . We have completed our model of the molecular gas chemistry in the M 82 nucleus . Our PDR chemical model successfully explains the [ CO ^ { + } ] / [ HCO ^ { + } ] ratios measured in the M 82 nucleus but fails by one order of magnitude to explain the large measured CO ^ { + } column densities ( \sim 1–4 \times 10 ^ { 13 } cm ^ { -2 } ) . We explore possible routes to reconcile the chemical model and the observations .