Conjecture 1 of Chang: "Positive scalar curvature of totally nonspin
manifolds" asserts that a closed smooth manifold M with non-spin universal
covering admits a metric of positive scalar curvature if and only if a certain
homological condition is satisfied. We present a counterexample to this
conjecture, based on the counterexample to the unstable Gromov-Lawson-Rosenberg
conjecture given in Schick: "A counterexample to the (unstable)
Gromov-Lawson-Rosenberg conjecture".