In this work, we present the model of plasmonic chrial nanolasers composed of aluminum-coated gallium-nitride (GaN) gammadions, which may lase with a high degree of circular polarization at room temperatures. Using the finite-element method, we examine resonant modes of the four-fold rotationally symmetric cavities of gammadions whose resonant frequencies lie in the gain spectrum of GaN. We find a degenerate doublet of resonant modes which can couple to plane waves in the far-field zone above gammadions. Their near-field profiles exhibit localized distribution in the arms of gammadions and a Fabry-Perot standing-wave pattern along the post. In practice, fabrication imperfections would inevitably spoil the four-fold rotation symmetry of gammadions. Typical perturbation could lift the degeneracy of doublet and leads to mixing of the two degenerate modes which may still output signals with observable handedness above gammadions. Considering a gammadion cavity with a single elongated arm, we show that the magnitude of dissymmetry factor of its resonant mode can be larger than unity. Our calculations are consistent with the experimental results, indicating that the right-handed gammadion cavities lase with a magnitude of dissymmetry factors near 1 at a wavelength of 364 nm. The dimensionless effective mode volume scaled by the cube of effective wavelength is 2.62, reflecting a modal distribution remarkably confined in the plasmonic structures and the capability of enhancing the spontaneous-emission rate noticeably. These chiral nanolasers with an ultrasmall footprint could be potentially utilized as future circularly-polarized photon source at the chip level.