The paper reports the creation of an ultracold dense gas of 40K87Rb polar molecules using a single step of STIRAP (STImulated Raman Adiabatic Passage) via two-frequency laser irradiation. The polar molecular gas has a peak density of 10^12 cm^-3 and a translational temperature of 350 nK. The molecules have permanent electric dipole moments, measured via Stark spectroscopy, of 0.052(2) Debye for the triplet rovibrational ground state and 0.566(17) Debye for the singlet rovibrational ground state. The study demonstrates the efficient transfer of ultracold atoms into the rovibrational ground state of both the triplet and singlet electronic ground molecular potentials, preserving the high phase-space density of the initial gas. This work paves the way for exploring a wide range of many-body physics phenomena and quantum information processing using ultracold polar molecules.The paper reports the creation of an ultracold dense gas of 40K87Rb polar molecules using a single step of STIRAP (STImulated Raman Adiabatic Passage) via two-frequency laser irradiation. The polar molecular gas has a peak density of 10^12 cm^-3 and a translational temperature of 350 nK. The molecules have permanent electric dipole moments, measured via Stark spectroscopy, of 0.052(2) Debye for the triplet rovibrational ground state and 0.566(17) Debye for the singlet rovibrational ground state. The study demonstrates the efficient transfer of ultracold atoms into the rovibrational ground state of both the triplet and singlet electronic ground molecular potentials, preserving the high phase-space density of the initial gas. This work paves the way for exploring a wide range of many-body physics phenomena and quantum information processing using ultracold polar molecules.