Computer-generated volume holograms (CGVHs) are gradient refractive index (GRIN) devices that consist of a superposition of multiple periodic diffraction gratings. Fabrication of these components for the visible range is difficult due to the small length-scale requirements but is more tenable in the terahertz (THz), as the length scales become more practical (≥ 10-5 m). We successfully utilized polymer-based 3D additive rapid-prototyping technology to fabricate, to our knowledge, the world's first 3D THz CGVH in approximately 50 minutes, using $12 of consumables. This demonstration suggests that this technique could be extended to fabricate THz volumetric optics with arbitrary electromagnetic profiles.