  Using 586pb^-1 of e^+e^- collision data at E_CM = 4170MeV, produced at the
CESR collider and collected with the CLEO-c detector, we observe the process
e^+e^- --> pi^+ pi^- h_c(1P). We measure its cross section to be
15.6+-2.3+-1.9+-3.0pb, where the third error is due to the external uncertainty
on the branching fraction of psi(2S) --> pi^0 h_c(1P), which we use for
normalization. We also find evidence for e^+e^- --> eta h_c(1P) at 4170MeV at
the 3sigma level, and see hints of a rise in the e^+e^- --> pi^+ pi^- h_c(1P)
cross section at 4260MeV.
