A study of the lineshape of the $chi_{c1}(3872)$ state is made using a data sample corresponding to an integrated luminosity of $3,$fb$^{-1}$ collected in $pp$ collisions at centre-of-mass energies of 7 and 8,TeV with the LHCb detector. Candidate $chi_{c1}(3872)$ and $psi(2S)$ mesons from b-hadron decays are selected in the $ J/psi pi^+ pi^-$ decay mode. Describing the {mbox{lineshape}} with a Breit--Wigner function, the mass splitting between the $chi_{c1}(3872)$ and $psi(2S)$ states, $Delta m$, and the width of the $chi_{c1}(3872)$ state, $Gamma_{mathrm{BW}}$, are determined to be begin{eqnarray*} Delta m & = & 185.598 pm 0.067 pm 0.068, mathrm{MeV} ,, Gamma_{mathrm{BW}} & = & phantom{00}1.39phantom{0} pm 0.24phantom{0} pm 0.10phantom{0} mathrm{MeV} ,, end{eqnarray*} where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired model, the mode and full width at half maximum of the lineshape are determined to be begin{eqnarray*} mathrm{mode} & = 3871.69^{,+,0.00,+,0.05}_{,-,0.04,-,0.13} &mathrm{MeV} mathrm{FWHM} & = 0.22^{,+,0.07,+,0.11}_{,-,0.06,-,0.13}& mathrm{MeV} . end{eqnarray*} An investigation of the analytic structure of the Flatte amplitude reveals a pole structure, which is compatible with a quasi-bound $D^0bar{D}^{*0}$ state but a quasi-virtual state is still allowed at the level of $2$ standard deviations.
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