Additive Manufacturing (AM) of low-profile 2.5D glass structures has been demonstrated using a fiber-fed laser-heated process. In this process, glass fibers with diameters 90-125 μm are supported as they are fed into the intersection of the workpiece and a CO2 laser beam. The workpiece is positioned by a four-axis CNC stage with coordinated rotational/transitional kinematics. The laser energy at λ = 10.6 μm is coupled to phonon modes in the glass, locally heating it above its working point. The rapid heating and cooling process allows for the deposition of various glasses into free-standing three-dimensional structures such as trusses and other complex geometries. Issues unique to the process are discussed, including the thermal breakdown of the glass and index inhomogeneity between the fiber core and cladding when using single-mode optical fiber feedstock.