We report the early discovery and multicolor (BVI) high-cadence light-curve analyses of the rapidly declining sub-Chandrasekhar Type Ia supernova KSP-OT-201509b (= AT 2015cx) from the KMTNet Supernova Program. The Phillips and color stretch parameters of KSP-OT-201509b are {Delta}M_B,15_~1.62mag and s_BV_~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 a 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+/-0.01M_{sun} of synthesized ^56^Ni mass, 0.84+/-0.12M{sun}_ of ejecta mass, and (0.61+/-0.14)x10^51^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 ~28mag/arcsec^2^ makes KSP-OT-201509b a hostless Type Ia supernova and offers new insights into supernova host galaxy environments.