We present experimental 2D IR spectra of isotope diluted ice Ih (i.e., the OH stretch mode of HOD in D2O and the OD stretch mode of HOD in H2O) at T = 80 K. The main spectral features are the extremely broad 1-2 excited state transition, much broader than the corresponding 0-1 groundstate transition, as well as the presence of quantum beats. We do not observe any inhomogeneous broadening that might be expected due to proton disorder in ice Ih. Complementary, we perform simulations in the framework of the Lippincott-Schroeder model, which qualitatively reproduce the experimental observations. We conclude that the origin of the observed line shape features is the coupling of the OH-vibrational coordinate with crystal phonons and explain the beatings as a coherent oscillation of the O⋅⋅⋅O hydrogen bond degree of freedom.