We report a search for the flavor-changing neutral current decay B-->K(*)l+l- using a 29.1 fb(-1) data sample accumulated at the Upsilon(4S) resonance with the Belle detector at the KEKB e+e- storage ring. We observe the decay process B-->Kl+l-(l = e, mu), for the first time, with a branching fraction of B(B-->Kl+l-) = (0.75(+0.25)(-0.21)+/-0.09)x10(-6).