  We present the H$\alpha$ intensity map of the host galaxy of the repeating
fast radio burst FRB 121102 at a redshift of z=0.193 obtained with the
AO-assisted Kyoto 3DII optical integral-field unit mounted on the 8.2-m Subaru
Telescope. We detected a compact H$\alpha$-emitting (i.e., star-forming) region
in the galaxy, which has a much smaller angular size [$< 0".57$ (1.9 kpc) at
full width at half maximum (FWHM)] than the extended stellar continuum emission
region determined by the Gemini/GMOS z'-band image [$\simeq 1".4$ (4.6 kpc) at
FWHM with ellipticity b/a=0.45]. The spatial offset between the centroid of the
H$\alpha$ emission region and the position of the radio bursts is $0".08 \pm
0".02$ ($0.26 \pm 0.07$ kpc), indicating that FRB 121102 is located within the
star-forming region. This close spatial association of FRB 121102 with the
star-forming region is consistent with expectations from young pulsar/magnetar
models for FRB 121102, and it also suggests that the observed H$\alpha$
emission region can make a major dispersion measure (DM) contribution to the
host galaxy DM component of FRB 121102. Nevertheless, the largest possible
value of the DM contribution from the H$\alpha$ emission region inferred from
our observations still requires a significant amount of ionized baryons in
intergalactic medium (the so-called `missing' baryons) as the DM source of FRB
121102, and we obtain a 90\% confidence level lower limit on the cosmic baryon
density in the intergalactic medium in the low-redshift universe as
$\Omega_{IGM} > 0.012$.
