We characterize computationally a red fluorescent protein (RFP) with the chromophore (Chro) sandwiched between two aromatic tyrosine rings in a triple-decker motif. According to the original proposal [J. Phys. Chem. Lett. 2013, 4, 1743], such a tyrosine-chromophoretyrosine pi-stacked construct can be accommodated in the green fluorescent protein (GFP). A recent study [ACS Chem. Biol. 2016, 11, 508] attempted to realize the triple-decker motif and obtained an RFP variant called mRojoA-VYGV with two tyrosine residues surrounding the chromophore. The crystal structure showed that only a tyrosine-chromophore pair was involved in 7r-stacking, whereas the second tyrosine was oriented perpendicularly, edge-to-face with respect to the chromophore. We propose a more promising variant of this RFP with a perfect triple-decker unit achieved by introducing additional mutations in mRojoA-VYGV. The structures and optical properties of model proteins based on the structures of mCherry and mRojoA are characterized computationally by QM(DFT)/MM. The electronic transitions in the protein-bound chromophores are computed by high-level quantum chemical methods. According to our calculations, the triple-decker chromophore unit in the new RFP variant is stable within the protein and its optical bands are red-shifted with respect to the parent mCherry and mRojoA species.