Selective laser melting (SLM) is a technique for the additive manufacturing (AM) of metals, plastics, and even ceramics. This paper explores using SLM for depositing glass structures. A CO2 laser is used to locally melt portions of a powder bed to study the effects of process parameters on stationary particle formation as well as continuous line quality. Numerical modeling is also applied to gain insight into the physical process. The experimental and numerical results indicate that the absorptivity of the glass powder is nearly constant with respect to the processing parameters. These results are used to deposit layered single-track wide walls to demonstrate the potential of using the SLM process for building transparent parts. Finally, the powder bed process is compared to a wire-fed approach. AM of glass is relevant for gradient index optics, systems with embedded optics, and the formation of hermetic seals.