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.
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