  We report the early discovery and multi-color ($BVI$) high-cadence light
curve analyses of a rapidly-declining sub-Chandrasekhar Type Ia supernova
KSP-OT-201509b (= AT2015cx) from the KMTNet Supernova Program. The Phillips
parameter and color stretch parameter of KSP-OT-201509b (= AT2015cx) are
$\Delta$$M_{B,15}$ $\simeq$ 1.62 mag and $s_{BV}$ $\simeq$ 0.54, respectively,
at an inferred redshift of 0.072. These, together with other measured
parameters (such as the strength of the secondary $I$-band peak, colors and
luminosity), identify the source to be a rapidly-declining Type Ia of
transitional nature that is closer to Branch Normal than 91bg-like. Its early
light curve evolution and bolometric luminosity are consistent with those of
homologously expanding ejecta powered by radioactive decay and a Type Ia SN
explosion with 0.32 $\pm$ 0.01 $M_{\odot}$ of synthesized $^{56}$Ni mass, 0.84
$\pm$ 0.12 $M_{\odot}$ of ejecta mass and (0.61 $\pm$ 0.14) $\times$ 10$^{51}$
erg of ejecta kinetic energy. While its $B-V$ and $V-I$ colors evolve largely
synchronously with the changes in the $I$-band light curve as found in other
supernovae, we also find the presence of an early redward evolution in $V-I$
prior to --10 days since peak. The bolometric light curve of the source is
compatible with a stratified $^{56}$Ni distribution extended to shallow layers
of the exploding progenitor. Comparisons between the observed light curves and
those predicted from ejecta-companion interactions clearly disfavor Roche
Lobe-filling companion stars at large separation distances, thus supporting a
double-degenerate scenario for its origin. The lack of any apparent host galaxy
in our deep stack images reaching a sensitivity limit of $\sim$ 28 $\rm
mag\;arcsec^{-2}$ makes KSP-OT-201509b a hostless Type Ia supernova and offers
new insights into supernova host galaxy environments.
