  We present a calculation of the Vector Form Factor at the next-to-leading
order in the 1/N_C expansion, within the framework of Resonance Chiral Theory.
The calculation is performed in the chiral limit, and with two dynamical quark
flavours. The ultraviolet behaviour of quantum loops involving virtual
resonance propagators is analyzed, together with the kind of counterterms
needed in the renormalization procedure. Using the lowest-order equations of
motion, we show that only a few combinations of local couplings appear in the
final result. The low-energy limit of our calculation reproduces the standard
Chiral Perturbation Theory formula, allowing us to determine the resonance
contribution to the chiral low-energy couplings, at the next-to-leading order
in 1/N_C, keeping a full control of their renormalization scale dependence.
