Cloning by the transplantation of somatic nuclei into unfertilized eggs requires a dramatic remodeling of chromosomal architecture. Many proteins are specifically lost from nuclei, and others are taken up from the egg cytoplasm. Recreating this exchange in vitro, we identified the chromatin-remodeling nucleosomal adenosine triphosphatase (ATPase) ISWI as a key molecule in this process. ISWI actively erases the TATA binding protein from association with the nuclear matrix. Defining the biochemistry of global nuclear remodeling may facilitate the efficiency of cloning and other dedifferentiation events that establish new stem cell lineages.