In this letter we consider Andreev tunnelling between a normal metal a
nd a one-dimensional Josephson junction array with finite-range Coulom
b energy. The I-V characteristics strongly deviate from the classical
linear Andreev current. We show that the non-linear conductance posses
ses interesting scaling behaviour when the chain undergoes a T = 0 sup
erconductor-insulator transition. When the chain is superconducting, t
he low-lying excitations are gapless and the I-V curves are power law.
When the chain is insulating the Andreev current is blocked up to a t
hreshold voltage, proportional to the inverse correlation length of th
e chain, which vanishes at the transition point.