We present the first evidence of charmless decays of the B(0)(s) meson, the decay B(0)(s)--> phiphi, and a measurement of the branching ratio BR(B(0)(s)--> phiphi) using 180 pb(-1) of data collected by the CDF II experiment at the Fermilab Tevatron collider. In addition, the BR and direct CP asymmetry for the B+-->phiK+ decay are measured. We obtain BR(B(0)(s)--> phiphi)=[14(+6)(-5)(stat)+/-6(syst)] x 10(-6), BR(B+-->phiK+)=[7.6+/-1.3(stat)+/-0.6(syst)] x 10(-6), and A(CP)(B+-->phiK+)= -0.07+/-0.17(stat)+0.03 / -0.02(syst). Both decays are governed in the standard model by second order (penguin) b-->s(-)ss amplitudes.