The adapted DIRAC experiment at the CERN PS accelerator observed for the first time long-lived hydrogenlike π^{+}π^{-} atoms, produced by protons hitting a beryllium target. A part of these atoms crossed the gap of 96 mm between the target and a 2.1 μm thick platinum foil, in which most of them dissociated. Analyzing the observed number of atomic pairs, n_{A}^{L}=436_{-61}^{+157}|_{tot}, the lifetime of the 2p state is found to be τ_{2p}=(0.45_{-0.30}^{+1.08}|_{tot})×10^{-11} s, not contradicting the corresponding QED 2p state lifetime τ_{2p}^{QED}=1.17×10^{-11} s. This lifetime value is three orders of magnitude larger than our previously measured value of the π^{+}π^{-} atom ground state lifetime τ=(3.15_{-0.26}^{+0.28}|_{tot})×10^{-15} s. Further studies of long-lived π^{+}π^{-} atoms will allow us to measure energy differences between p and s atomic states and so to discriminate between the isoscalar and isotensor ππ scattering lengths with the aim to check QCD predictions.