A couple months ago, I inquired if anyone knew anything about oriented singular homology. Not receiving any replies, I worked on the question myself. The answer is in the abstract below. Let C_n denote the nth singular chain functor on the category of topological spaces. Viewing C_n as the free abelian group on the functor represented by Delta_n = {(t_0,...,t_n) | t_i >= 0 and t_0 + ... + t_n = 1}, it is clear there is a right action of the permutation group Sigma_{n+1} by composition. Let U_n be the set of all sigma p - sgn(p) sigma for sigma a singular n-simplex and p a permutation. Let V_n consist of U_n together with all simplexes sigma such that sigma = sigma p for some transposition p and let W_n consist of U_n together with all simplexes sigma such that sigma = sigma p for some odd permutation p. Then U, V and W are subcomplexes and all the maps in C --> C/U --> C/V --> C/W are homtopy equivalences (with natural transformations for the homotopy inverses as well as the homotopies themselves. The proof uses the original cotriple cyclic models theorem that Jon Beck and I proved in 1965.