Abstract: We introduce a completion tower for algebras over operads in unbounded chain complexes (resp. symmetric spectra) and prove that under appropriate connectivity conditions this tower interpolates between Quillen homology and the identity functor. This talk will focus on the chain complex version of these results, beginning with a short introduction to Quillen's notion of derived abelianization, and followed by a sketch of the proof with an emphasis on several of the homotopical arguments. We will illustrate the tower results in the special case of commutative differential graded algebras and André-Quillen homology. These results are joint work with K. Hess.