We discuss a cosmology in which cold dark-matter particles decay into relativistic particles. We argue that such decays could lead naturally to a bulk viscosity in the cosmic fluid. For decay lifetimes comparable to the present hubble age, this bulk viscosity enters the cosmic energy equation as an effective negative pressure. We investigate whether this negative pressure is of sufficient magnitude to account fo the observed cosmic acceleration. We show that a single decaying species in a Λ = 0, flat, dark-matter dominated cosmology can not reproduce the observed magnituderedshift relation from Type Ia supernovae. However, a delayed bulk viscosity, possibly due to a cascade of decaying particles may be able to account for a significant fraction of the apparent cosmic acceleration. Possible candidate nonrelativistic particles for this scenario include sterile neutrinos or gauge-mediated decaying supersymmetric particles.PACS numbers: 98.80. Cq, 95.30.Cq, 95.35.+d, 95.36.+x, 98.80.Es, 98.62.Py