We present studies of the photoexcited quasiparticle dynamics in Tl(2)Ba(2)Ca(2)Cu(3)O(y) (Tl-2223) using femtosecond optical techniques. Deep into the superconducting state (below 40 K), a dramatic change occurs in the temporal dynamics associated with photoexcited quasiparticles rejoining the condensate. This is suggestive of entry into a coexistence phase which, as our analysis reveals, opens a gap in the density of states (in addition to the superconducting gap), and furthermore, competes with superconductivity resulting in a depression of the superconducting gap.