The $overline{B_s^0} rightarrow chi_{c2} K^+ K^- $ decay mode is observed and its branching fraction relative to the corresponding $chi_{c1}$ decay mode, in a $pm 15 textrm{MeV}/c^2$ window around the $phi$ mass, is found to be $frac{mathcal{B}(overline{B_s^0} rightarrow chi_{c2} K^+ K^-) }{ mathcal{B}(overline{B_s^0} rightarrow chi_{c1} K^+ K^-)} = (17.1 pm 3.1 pm 0.4 pm 0.9)%,$ where the first uncertainty is statistical, the second systematic and the third due to the knowledge of the branching fractions of radiative $chi_c$ decays. The decay mode $overline{B_s^0} rightarrow chi_{c1} K^+ K^- $ allows the $ B_s^0$ mass to be measured as $m(B_s^0) = 5366.83 pm 0.25 pm 0.27 , textrm{MeV}/c^2,$ where the first uncertainty is statistical and the second systematic. A combination of this result with other LHCb determinations of the $B_s^0$ mass is made.
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