The creation of millimeter wave, 3D-printable dielectric nanocomposite is demonstrated. Alumina nanoparticles were combined with styrenic block copolymers and solvent to create shear thinning, viscoelastic inks that are printable at room temperature. Particle loadings of up to 41 vol % were achieved. Upon being dried, the highest-performing of these materials has a permittivity of 4.61 and a loss tangent of 0.00298 in the Ka band (26.5-40 GHz), a combination not previously demonstrated for 3D printing. These nanocomposite materials were used to print a simple resonator device with predictable pass-band features.