We report evidence for the decay mode B-->phiphiK based on an analysis of 78 fb(-1) of data collected with the Belle detector at KEKB. This is the first example of a b-->sssss transition. The branching fraction for this decay is measured to be B(B+/--->phiphiK+/-)=(2.6(+1.1)(-0.9)+/-0.3)x10(-6) for a phiphi invariant mass below 2.85 GeV/c(2). Results for other related charmonium decay modes are also reported.