Results on two-particle angular correlations for charged particles emitted in pPb collisions at a nucleon–nucleon center-of-mass energy of 5.02 TeV are presented. The analysis uses two million collisions collected with the CMS detector at the LHC. The correlations are studied over a broad range of pseudorapidity, η, and full azimuth, ϕ, as a function of charged particle multiplicity and particle transverse momentum, pT. In high-multiplicity events, a long-range (2<|Δη|<4), near-side (Δϕ≈0) structure emerges in the two-particle Δη–Δϕ correlation functions. This is the first observation of such correlations in proton–nucleus collisions, resembling the ridge-like correlations seen in high-multiplicity pp collisions at s=7TeV and in AA collisions over a broad range of center-of-mass energies. The correlation strength exhibits a pronounced maximum in the range of pT=1–1.5GeV/c and an approximately linear increase with charged particle multiplicity for high-multiplicity events. These observations are qualitatively similar to those in pp collisions when selecting the same observed particle multiplicity, while the overall strength of the correlations is significantly larger in pPb collisions.