To avoid electrostatic charging of an insulating matrix an electrical conductivity above sigma = 10(-6) Sm-1 is needed. At present, the most common practice to achieve this conductivity is to use a conductive filler such as carbon black. In this work, untreated catalytically-grown carbon nanotubes were dispersed in an epoxy matrix. After curing the epoxy, the electrical properties of the composite were measured in order to relate the filler volume fraction to the electrical conductivity. The intense stirring process used to disperse the carbon nanotubes has made it possible to achieve a matrix conductivity around sigma = 10(-2) Sm-1 with filler volume fractions as low as 0.1 vol.%. These figures represent an advance on best conductivity values previously obtained with carbon black in the same epoxy matrix. These low filler fractions ensure that the mechanical properties of the matrix are not compromised.