The B$_\mathrm{c}^+$ meson is observed for the first time in heavy ion collisions. Data from the CMS detector are used to study the production of the B$_\mathrm{c}^+$ meson in lead-lead (PbPb) and proton-proton (pp) collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_{\mathrm{NN}}} =$ 5.02 TeV, via the B$_\mathrm{c}^+$ $\to$ (J/$\psi$ $\to$ $\mu^+\mu^-$)$\mu^+\nu_\mu$ decay. The B$_\mathrm{c}^+$ nuclear modification factor, derived from the PbPb-to-pp ratio of production cross sections, is measured in two bins of the trimuon transverse momentum and of the PbPb collision centrality. The B$_\mathrm{c}^+$ meson is shown to be less suppressed than quarkonia and most of the open heavy-flavor mesons, suggesting that effects of the hot and dense nuclear matter created in heavy ion collisions contribute to its production. This measurement sets forth a promising new probe of the interplay of suppression and enhancement mechanisms in the production of heavy-flavor mesons in the quark-gluon plasma.