We report evidence of dense, ordered nanodomains in single-component fluid lipid bilayers. Our atomic-scale molecular dynamics simulations suggest that the area available to a lipid acyl chain exhibits large fluctuations, resulting in denser and sparser domains. The sizes of the dense domains can be up to approximately 10 nm, and their lifetimes are of the order of approximately 10 ns. In addition, our simulations suggest that domains of lipids with highly ordered acyl chains form predominantly within the dense regions, their sizes ranging from a few chains up to a few nanometers, and with lifetimes between approximately 10 ps-10 ns. These observations shed light on the origin of experimentally observed fluctuations, as well as on the mechanisms of phase transitions in lipid membranes.