The B_{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_{c}^{+} meson in lead-lead (Pb-Pb) and proton-proton (pp) collisions at a center-of-mass energy per nucleon pair of sqrt[s_{NN}]=5.02 TeV, via the B_{c}^{+}→(J/ψ→μ^{+}μ^{-})μ^{+}ν_{μ} decay. The B_{c}^{+} nuclear modification factor, derived from the Pb-Pb-to-pp ratio of production cross sections, is measured in two bins of the trimuon transverse momentum and of the Pb-Pb collision centrality. The B_{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.