To investigate the implications of the unique properties of fullerenes on their interaction with and passive transport into lipid membranes, atomistic molecular dynamics simulations of a C60 fullerene in a fully hydrated di-myristoyl-phoshatidylcholine lipid membrane have been carried out. In these simulations the free energy and the diffusivity of the fullerene were obtained as a function of its position within the membrane. These properties were utilized to calculate the permeability of fullerenes through the lipid membrane. Simulations reveal that the free energy decreases as the fullerene passes from the aqueous phase, through the head group layer and into the hydrophobic core of the membrane. This decrease in free energy is not due to hydrophobic interactions but rather to stronger van der Waals (dispersion) interactions between the fullerene and the membrane compared to those between the fullerene and (bulk) water. It was found that there is no free energy barrier for transport of a fullerene from the aqueous phase into the lipid core of the membrane. In combination with strong partitioning of the fullerenes into the lipidic core of the membrane, this "barrierless" penetration results in an astonishingly large permeability of fullerenes through the lipid membrane, greater than observed for any other known penetrant. When the strength of the dispersion interactions between the fullerene and its surroundings is reduced in the simulations, thereby emulating a nanometer sized hydrophobic particle, a large free energy barrier for penetration of the head group layer emerges, indicating that the large permeability of fullerenes through lipid membranes is a result of their unique interaction with their surrounding medium.