Little is known of Molloy’s early life, other than he was born in Scotland and studied law before emigrating to the United States, then working as a surveyor in North Carolina. In 1784 the legislature of North Carolina passed an act establishing the Town of Nashville, and Malloy was tasked with creating the first survey of lots in the new frontier town, endowing it with its initial urban form. The original survey map is lost, but a second survey completed for John Overton in 1789 features a village plat of one-acre lots. Four acres were reserved for a civic square (now Public Square) on the bluffs along the Cumberland River. Molloy superimposed a grid upon the undulating terrain without regard for topographical variations, a pattern which is still evident in the present layout of Nashville’s downtown streets.
As one of the five trustees appointed to handle the business of the town, Molloy also received a wooded, 1,600-acre tract along the river. Although he had substantial land holdings in North Carolina, he relocated to Nashville and by 1785 had established a law practice there. He was appointed Justice of the Peace for Davidson County in 1790. Mollloy fathered several children with an enslaved woman whom he owned. After reportedly becoming increasingly concerned for the welfare of his biracial daughter Sophia, he left his estate to be managed by trustees (including John Overton) whom he asked to care for her. Molloy is believed to have died in 1801, although his age and place of burial remain unknown.