Using a newly synthesized gibberellin analog containing an acetoxymethyl group (GA(3)-AM) and its binding proteins, we developed an efficient chemically inducible dimerization (CID) system that is completely orthogonal to existing rapamycin-mediated protein dimerization. Combining the two systems should allow applications that have been difficult or impossible with only one CID system. By using both chemical inputs (rapamycin and GA(3)-AM), we designed and synthesized Boolean logic gates in living mammalian cells. These gates produced output signals such as fluorescence and membrane ruffling on a timescale of seconds, substantially faster than earlier intracellular logic gates. The use of two orthogonal dimerization systems in the same cell also allows for finer modulation of protein perturbations than is possible with a single dimerizer.