We work in the locally de Sitter background of an inflating universe and consider a massless, minimally coupled scalar with a quartic self-interaction. We use dimensional regularization to compute the fully renormalized scalar self-mass-squared at one- and two-loop order for a state which is released in Bunch-Davies vacuum at t = 0. Although the field strength and coupling constant renormalizations are identical to those of flat space, the geometry induces a non-zero mass renormalization. The finite part also shows a sort of growing mass that competes with the classical force in eventually turning off this system's super-acceleration.