We report measurements of the magnetoresistance of long (> 50 mum), na
rrow (< 1 mum) quantum wires fabricated from a high mobility two-dimen
sional electron gas. We observe that, at low filling factors, the Shub
nikov-de Haas oscillations split into a series of sharp peaks which we
attribute to resonant tunnelling between edge states through localize
d states in the bulk. The results are in excellent agreement with the
theoretical model of Jain and Kivelson.