Would a Deeply Bound $b\bar b b\bar b$ Tetraquark Meson be Observed at the LHC?

There has been much theoretical speculation about the existence of a deeply bounded tetra-bottom state. Such a state would not be expected to be more than a GeV below $\Upsilon\Upsilon$ threshold. If such a state exists below the $\eta_b\eta_b$ threshold it would be narrow, as Zweig allowed strong decays are kinematically forbidden. Given the observation of $\Upsilon$ pair production at CMS, such a state with a large branching fraction into $\Upsilon \Upsilon^*$ is likely discoverable at the LHC. The discovery mode is similar to the SM Higgs decaying into four leptons through the $Z Z^*$ channel. The testable features of both production and the four lepton decays of such a tetra-bottom ground state are presented. The assumptions required for each feature are identified, allowing the application of our results more generally to a resonance decaying into four charged leptons (through the $\Upsilon\Upsilon^*$ channel) in the same mass region.