Low‐temperature absorption, fluorescence and persistent nonphotochemical hole‐burned spectra are reported for the CP29 chlorophyll (Chl) a/b antenna complex of photosystem II of green plants. The absorption‐origin band of the lowest Qy‐state lies at 678.2 nm and carries a width of ∼130 cm−1 that is dominated by inhomogeneous broadening at low temperatures. Its absorption intensity is equivalent to that of one of the six Chl a molecules of CP29. The absence of a significant satellite hole structure produced by hole burning, within the absorption band of the lowest state, indicates that the associated Chl a molecule is weakly coupled to the other Chl and, therefore, that the lowest‐energy state is highly localized on a single Chl a molecule. The electron–phonon coupling of the 678.2 nm state is weak with a Huang–Rhys factor S of 0.5 and a peak phonon frequency (ωm) of ∼20 cm−1. These values give a Stokes shift (2Sωm) in good agreement with the measured positions of the absorption band at 678.2 nm and a fluorescence‐origin band at 679.1 nm. Zero‐phonon holes associated with the lowest state have a width of ∼0.05 cm−1 at 4.2 K, corresponding to a total effective dephasing time of ∼400 ps. The temperature dependence of the zero‐phonon holewidth indicates that this time constant is dominated at temperatures below 8 K by pure dephasing/spectral diffusion due to coupling of the optical transition to the glass‐like two‐level systems of the protein. Zero‐phonon holewidths obtained for the Chl b bands at 638.5 and 650.0 nm, at 4.2 K, lead to lower limits of 900 ± 150 fs and 4.2 ± 0.3 ps, respectively, for the Chl b→ Chl a energy‐transfer times. Downward energy transfer from the Chl a state(s) at 665.0 nm occurs in 5.3 ± 0.6 ps at 4.2 K.