Cell shape and membrane remodeling rely on regulated interactions between the lipid bilayer and cytoskeletal arrays at the cell cortex. During cytokinesis, animal cells build an actomyosin ring anchored to the plasma membrane at the equatorial cortex. Ring constriction coupled to plasma-membrane ingression separates the two daughter cells. Plasma-membrane lipids influence membrane biophysical properties such as membrane curvature and elasticity and play an active role in cell function, and specialized membrane domains are emerging as important factors in regulating assembly and rearrangement of the cytoskeleton. Here, we show that mutations in the gene bond, which encodes a Drosophila member of the family of Elovl proteins that mediate elongation of very-long-chain fatty acids, block or dramatically slow cleavage-furrow ingression during early telophase in dividing spermatocytes. In bond mutant cells at late stages of division, the contractile ring frequently detaches from the cortex and constricts or collapses to one side of the cell, and the cleavage furrow regresses. Our findings implicate very-long-chain fatty acids or their derivative complex lipids in allowing supple membrane deformation and the stable connection of cortical contractile components to the plasma membrane during cell division.