We study the Kondo Lattice and the Hubbard models on a triangular lattice. We find that at the mean-field level, these rotationally invariant models naturally support a noncoplanar chiral magnetic ordering. It appears as a weak-coupling instability at the band filling factor 3/4 due to the perfect nesting of the itinerant electron Fermi surface. This ordering is a triangular-lattice counterpart of the collinear Neel ordering that occurs on the half-filled square lattice. While the long-range magnetic ordering is destroyed by thermal fluctuations, the chirality can persist up to a finite temperature, causing a spontaneous quantum Hall effect in the absence of any externally applied magnetic field.