We report the identification from multi-wavelength observations of the Fermi Large Area Telescope ( LAT ) source 4FGL J1405.1-6119 ( = 3FGL J1405.4-6119 ) as a high-mass gamma-ray binary . Observations with the LAT show that gamma-ray emission from the system is modulated at a period of 13.7135 \pm 0.0019 days , with the presence of two maxima per orbit with different spectral properties . X-ray observations using the Neil Gehrels Swift Observatory X-ray Telescope ( XRT ) show that X-ray emission is also modulated at this period , but with a single maximum that is closer to the secondary lower-energy gamma-ray maximum . A radio source , coincident with the X-ray source is also found from Australia Telescope Compact Array ( ATCA ) observations , and the radio emission is modulated on the gamma-ray period with similar phasing to the X-ray emission . A large degree of interstellar obscuration severely hampers optical observations , but a near-infrared counterpart is found . Near-infrared spectroscopy indicates an O6 III spectral classification . This is the third gamma-ray binary to be discovered with the Fermi LAT from periodic modulation of the gamma-ray emission , the other two sources also have early O star , rather than Be star , counterparts . We consider at what distances we can detect such modulated gamma-ray emission with the LAT , and examine constraints on the gamma-ray binary population of the Milky Way .