A study of the lineshape of the χ c 1 ( 3872 ) state is made using a data sample corresponding to an integrated luminosity of 3 fb − 1 collected in p p collisions at center-of-mass energies of 7 and 8 TeV with the LHCb detector. Candidate χ c 1 ( 3872 ) and ψ ( 2 S ) mesons from b -hadron decays are selected in the J / ψ π + π − decay mode. Describing the lineshape with a Breit-Wigner function, the mass splitting between the χ c 1 ( 3872 ) and ψ ( 2 S ) states, Δ m , and the width of the χ c 1 ( 3872 ) state, Γ BW , are determined to be Δ m = 185.598 ± 0.067 ± 0.068 MeV , Γ BW = 1.39 ± 0.24 ± 0.10 MeV , where the first uncertainty is statistical and the second systematic. Using a Flatté-inspired model, the mode and full width at half maximum of the lineshape are determined to be mode = 3871.6 9 + 0.00 + 0.05 − 0.04 − 0.13 MeV , FWHM = 0.2 2 + 0.07 + 0.11 − 0.06 − 0.13 MeV . An investigation of the analytic structure of the Flatté amplitude reveals a pole structure, which is compatible with a quasibound D 0 ¯ D * 0 state but a quasivirtual state is still allowed at the level of 2 standard deviations.