3D concrete printing has the potential to provide solutions to the global shortage of affordable housing. The technology may be particularly suitable for remote regions, where the shortage of labor and materials present challenges. While most projects have focused on the use the technology to fabricate a structure’s walls, this article describes a research effort aimed at printing the entire structure, including the enclosing surface using only 3D concrete printing. The design of a habitat for the permafrost regions of Alaska is used as a case study. The design approach was to conceive a parametric housing system based on modular units whose form are inspired by traditional vault design and amenable to 3D concrete printing. The proposed design is based on features and reach of the robotic arm printer, the desire to avoid formwork, withstanding applicable loads on the structure, and thermal requirements. While the size of each modular unit is determined by spatial requirements, its exact shape is defined using optimization following structural, thermal, and printing considerations. The printing of a reduced-scale version of the proposed unit validated the design showing its printability.