The first evidence for X(3872) production in relativistic heavy ion collisions is reported. The X(3872) production is studied in lead-lead (Pb-Pb) collisions at a center-of-mass energy of sqrt[s_{NN}]=5.02 TeV per nucleon pair, using the decay chain X(3872)→J/ψπ^{+}π^{-}→μ^{+}μ^{-}π^{+}π^{-}. The data were recorded with the CMS detector in 2018 and correspond to an integrated luminosity of 1.7 nb^{-1}. The measurement is performed in the rapidity and transverse momentum ranges |y|<1.6 and 15<p_{T}<50 GeV/c. The significance of the inclusive X(3872) signal is 4.2 standard deviations. The prompt X(3872) to ψ2S yield ratio is found to be ρ^{Pb-Pb}=1.08±0.49(stat)±0.52(syst), to be compared with typical values of 0.1 for pp collisions. This result provides a unique experimental input to theoretical models of the X(3872) production mechanism, and of the nature of this exotic state.