  We construct a stacky curve of genus $1/2$ (i.e., Euler characteristic $1$)
over $\mathbb{Z}$ that has an $\mathbb{R}$-point and a $\mathbb{Z}_p$-point for
every prime $p$ but no $\mathbb{Z}$-point. This is best possible: we also prove
that any stacky curve of genus less than $1/2$ over a ring of $S$-integers of a
global field satisfies the local-global principle for integral points.
