  We find homogeneous counting quasimorphisms that are effective at seeing
chains in a free group F. As corollary, we derive that if a group G has an
index-d free subgroup, then every element g in G either has stable commutator
length at least 1/8d or some power of g is conjugate to its inverse. We also
show that for a finitely-generated free group F, there is a countable basis for
the real vector space of homogeneous quasimorphisms on F.
