This work reports a method for fabricating three-dimensional microwave metamaterials by fused deposition modeling 3D printing of a highly conductive polymer composite filament. The conductivity of such a filament is shown to be nearly equivalent to that of a perfect conductor for microwave metamaterial applications. The expanded degrees-of-freedom made available by 3D metamaterial designs are demonstrated by designing, fabricating, and testing a 3D-printed unit cell with a broadband permittivity as high as 14.4. The measured and simulated S-parameters agree well with a mean squared error smaller than 0.1. The presented method not only allows reliable and convenient fabrication of microwave metamaterials with high conductivity but also opens the door to exploiting the third dimension of the unit cell design space to achieve enhanced electromagnetic properties.