An outerplanar graph is a graph have a planar embedding with all
vertices on the unbounded face. A linear forest is a graph in which
every component is a path. Glenn Chappell conjectured that every
outerplanar graph has an induced subgraph with more than 4/7 of the
vertices that is a linear forest, and he provided examples to show that
this is best possible. We prove Chappell's conjecture.