  We simulate 3-flavour lattice QCD with a small chemical potential $\mu_I$ for
isospin, at temperatures close to the finite temperature transition. Using
quark masses just above the critical mass for zero chemical potential, we
determine the position of the transition from hadronic matter to a quark-gluon
plasma as a function of $\mu_I$. We see evidence for a critical endpoint where
the transition changes from a crossover to a first-order transition as $\mu_I$
is increased. We argue that QCD at finite $\mu_I$ and QCD at finite
quark-numberchemical potential $\mu$ should behave similarly in this region.
