Permeation of small molecules across cell membranes is a ubiquitous process in biology and is dependent on the principles of physical chemistry at the molecular level. Here we use atomistic molecular dynamics simulations to calculate the free energy of permeation of a range of small molecules through a model of the outer membrane of Escherichia coli, an archetypical Gram-negative bacterium. The model membrane contains lipopolysaccharide (LPS) molecules in the outer leaflet and phospholipids in the inner leaflet. Our results show that the energetic barriers to permeation through the two leaflets of the membrane are distinctly asymmetric; the LPS headgroups provide a less energetically favorable environment for organic compounds than do phospholipids. In summary, we provide the first reported estimates of the relative free energies associated with the different chemical environments experienced by solutes as they attempt to cross the outer membrane of a Gram-negative bacterium. These results provide key insights for the development of novel antibiotics that target these bacteria.