We show that chiral Frenkel excitons yield intense circularly polarized luminescence with an intrinsic dissymmetry factor in emission glum as high as 0.08. This outstanding value is measured through thin films of cyanine J-aggregates that form twisted bundles. Our measurements, obtained by a Mueller polarization analysis, are artifact-free and reveal a quasi-perfect correlation between the dissymmetry factors in absorption, gabs , and in emission glum . We interpret the bisignate dissymmetry factors as the signature of a strong coupling between chiral Frenkel excitons longitudinally excited along the bundles. We further resolve by polarimetry analysis the split in energy between the excited states with a Davydov splitting as small as 28 meV. We finally show the anti-Kasha nature of the chiral emission bands with opposite optical chirality. These mirror-imaged emissive chiroptical features emerge from the structural rigidity of the bundles that preserves the ground- and excited-state chirality.