  We show that the lightcone worldsheet formalism, constructed to represent the
sum of the bare planar diagrams of scalar \phi^3 field theory, survives the
renormalization procedure in space-time dimensions D not greater than 6.
Specifically this means that all the counter-terms, necessary to produce a
successful renormalized perturbation expansion to all orders, can be
represented as local terms in the lightcone worldsheet action. Because the
worldsheet regulator breaks Lorentz invariance, we find the need for two
non-covariant counter-terms, in addition to the usual mass, coupling and wave
function renormalization. One of these can be simply interpreted as a rescaling
of transverse coordinates with respect to longitudinal coordinates. The second
one introduces couplings between the matter and ghost worldsheet fields on the
boundaries.
