The $B_s^0 rightarrow J/psi phi phi$ decay is observed in $pp$ collision data corresponding to an integrated luminosity of 3 fb$^{-1}$ recorded by the LHCb detector at centre-of-mass energies of 7 TeV and 8 TeV. This is the first observation of this decay channel, with a statistical significance of 15 standard deviations. The mass of the $B_s^0$ meson is measured to be $5367.08,pm ,0.38,pm, 0.15$ MeV/c$^2$. The branching fraction ratio $mathcal{B}(B_s^0 rightarrow J/psi phi phi)/mathcal{B}(B_s^0 rightarrow J/psi phi)$ is measured to be $0.0115,pm, 0.0012, ^{+0.0005}_{-0.0009}$. In both cases, the first uncertainty is statistical and the second is systematic. No evidence for non-resonant $B_s^0 rightarrow J/psi phi K^+ K^-$ or $B_s^0 rightarrow J/psi K^+ K^- K^+ K^-$ decays is found.
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