The aim of this study is to investigate the edge chipping and surface roughness of basalt rock processed by rotary ultrasonic machining (RUM) using compressed air as coolant. Basalt rock is commonly used as a building and construction material for foundations and dams, as well as in architectural designs such as constructing thin veneers and facades. Rotary ultrasonic machining, a hybrid process of grinding and ultrasonic machining, is employed to drill difficult-to-machine materials such as ceramics, composites, titanium alloys, stainless steel, etc. RUM has many advantages over conventional machining processes such as twist drilling. These advantages include lower cutting force, higher surface quality, lower tool wear, etc. This paper is the first in literature to report a study on edge chipping and surface roughness on RUM of basalt rock using cold compressed air as coolant. The effects of three input variables (tool rotation speed, feedrate, and ultrasonic power) on cutting force, torque, edge chipping, and surface roughness were studied. Experimental results obtained from this investigation show that RUM with cold air as the coolant has the capability to machine holes in basalt rock with a surface roughness of less than 3.5 μm without severe edge chipping.