Let C_{TS} be the subgroup of the smooth knot concordance group generated by topologically slice knots. Endo showed that C_{TS} contains an infinite rank subgroup, and Livingston and Manolescu-Owens showed that C_{TS} contains a Z^3summand. We show that in fact C_{TS} contains a Z^\infty summand. The proof relies on the knot Floer homology package of Ozsvath-Szabo and the concordance invariant epsilon.