  For any group, there is a natural (pseudo-)norm on the vector space B1 of
real (group) 1-boundaries, called the stable commutator length norm. This norm
is closely related to, and can be thought of as a relative version of, the
Gromov (pseudo)-norm on (ordinary) homology. We show that for a free group, the
unit ball of this pseudo-norm is a rational polyhedron.
  It follows that stable commutator length in free groups takes on only
rational values. Moreover every element of the commutator subgroup of a free
group rationally bounds an injective map of a surface group.
  The proof of these facts yields an algorithm to compute stable commutator
length in free groups. Using this algorithm, we answer a well-known question of
Bavard in the negative, constructing explicit examples of elements in free
groups whose stable commutator length is not a half-integer.
