There has been tremendous interest in the Additive Manufacturing (AM) of polymers, metals, and ceramics leading to a wealth of research and development of these processes. By contrast, there has been little attention paid to AM processes for glass. This paper presents a custom-made glass additive machine. A CO2 laser is used to generate a molten pool of glass into which glass filaments are fed. A motion system is used to trace a layer, after which the build platform is lowered to fabricate the next layer. Two of the unique issues that must be addressed in the AM of glass are 1) various mechanisms can cause the formation of bubbles that deteriorate part optical and mechanical properties and 2) significant processing forces can move the melt pool away from its desired location. In this paper a melt pool temperature controller is designed to regulate the melt pool temperature at a constant value and a path and trajectory generation algorithm is constructed to maintain a constant glass filament feed direction relative to the scan velocity. The experimental results demonstrate that the melt pool temperature controller is able to avoid bubble formation over a wide range of build speeds and that the path planned directional-control is able to maintain good dimensional accuracy throughout closed contours. The capabilities of the AM for glass machine are demonstrated on a thin-walled, multi-layer star pattern and a spring in which the material is printed in freespace without the need for support structures.