The thermal conductivity of neon, over a wide pressure range up to 1000 MPa, is determined from ab initio calculations. A previous published ab initio potential for Ne2 is applied in an equilibrium molecular dynamics simulation. The thermal conductivity is obtained from the Green-Kubo integral. Comparisons with experiment show that the ab initio results do not deviate by more than 10% from the experimental values, the r.m.s. deviation being only 4.3% for ten values between 100 and 1000 MPa. As no fit parameters are used, this is a quite pleasing result for the first approach of its kind.