  Within the nonrelativistic QCD (NRQCD) factorization framework, we
investigate the inclusive production of the $h_c$ meson associated with either
light hadrons or charmed hadrons at $B$ factory energy $\sqrt{s}=10.58$ GeV.
Both the leading color-singlet and color-octet channels are included. For the
$h_c$ production associated with light hadrons, the total production rate is
dominated by the color-octet channel, thus the future measurement of this
process may impose useful constraint on the value of the color-octet matrix
element $<{\cal O}^{h_c}_8({}^1S_0)>$; for the $h_c$ production associated with
charmed hadrons, the total production rate is about one order of magnitude
smaller, and dominated by the color-singlet channel.
