We have analyzed data of the DISTO experiment on the exclusive pp --> pLambdaK+ reaction at 2.85 GeV to search for a strongly bound compact K- pp(approximately = X) state to be formed in the pp --> K+ + X reaction. The observed spectra of the K+ missing mass and the pLambda invariant-mass with high transverse momenta of p and K+ revealed a broad distinct peak of 26-sigma confidence with a mass M(X)=2267+/-3(stat)+/-5(syst) MeV/c2 and a width Gamma(X)=118+/-8(stat)+/-10(syst) MeV. The enormously large cross section indicates formation of a compact K- pp with a large binding energy of B(K)=103 MeV, which can be a possible gateway toward cold and dense kaonic nuclear matter.