Exclusive.(770) 0 photoproduction is measured for the first time in ultraperipheral pPb collisions at v s NN = 5.02 TeV with the CMS detector. The cross section s(.p..(770) 0 p) is 11.0 +/- 1.4 (stat) +/- 1.0 (syst) mu b at W. p = 92.6GeV for photon-proton centre-of-mass energies W. p between 29 and 213 GeV. The differential cross section ds/d| t| is measured in the interval 0.025 <| t| <1GeV 2 as a function of W. p, where t is the squared four-momentum transfer at the proton vertex. The results are compared with previous measurements and theoretical predictions. The measured cross section s(.p..(770) 0 p) has a power-law dependence on the photon-proton centre-of-mass, consistent with electron-proton collision measurements performed at HERA. The W. p dependence of the exponential slope of the differential cross section ds/d| t| is also measured.