We present evidence for the first observation of electromagnetically bound π ± K ∓ -pairs (πK-atoms) with the DIRAC-II experiment at the CERN-PS. The πK-atoms are produced by the 24 GeV/c proton beam in a thin Pt-target and the dissociated π ± and K ∓ -mesons analyzed in a two-arm magnetic spectrometer. The observed enhancement at low relative momentum corresponds to the production of 173±54 πK-atoms. The mean life of πK-atoms is related to the s-wave πK-scattering lengths. From these first data we derive a lower limit for the mean life of 1.5 fs at 84% confidence level.