The quantum numbers of the X(3872) meson are determined to be J(PC) = 1(++) based on angular correlations in B+ -> X(3872)K+ decays, where X(3872) -> pi(+) pi(-) j/psi and J/psi -> pi(+) mu(-). The data correspond to 1.0 fb(-1) of pp collisions collected by the LHCb detector. The only alternative assignment allowed by previous measurements J(PC) = 2(-+) is rejected with a confidence level equivalent to more than 8 Gaussian standard deviations using a likelihood-ratio test in the full angular phase space. This result favors exotic explanations of the X(3872) state.