There are many scientific and engineering applications of transparent glass including optics, communications, electronics, and hermetic seals. However, there has been minimal research towards the Additive Manufacturing (AM) of transparent glass parts. This paper describes and demonstrates a filament-fed technique for AM of transparent glass. A transparent glass filament is melted by a CO2 laser and solidifies as the workpiece is translated relative to the stationary laser beam. To prevent thermal shock, the workpiece rests on a heated build platform. In order to obtain optically transparent parts, several challenges must be overcome, notably producing index homogeneity and avoiding bubble formation. The effects of key process parameters on the morphology and transparency of the printed glass are explored experimentally. These results are compared to a low order model relating the process parameters to the temperature of the molten region, which is critical to the quality of the deposited glass. At lower temperatures, the glass is not fully melted, resulting in index variations in the final part, while at higher temperatures, phase separation introduces bubbles and other defects into the part. The correct process avoids these issues and deposits optically transparent glass.