  We present the detection of the reactive ion CO+ towards 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 650pc of the nuclear disk of M82. Such high values of the [CO+]/[HCO+]
ratio had only been previously measured towards the atomic peak in the
reflection nebula NGC7023. This detection corroborates that the molecular gas
reservoir in the M82 disk is heavily affected by the UV radiation from the
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
M~82 nucleus but fails by one order of magnitude to explain the large measured
CO+ column densities (~1--4x10^{13} cm^{-2}). We explore possible routes to
reconcile the chemical model and the observations.
