Deuterium (D) is one of the light elements created in the Big Bang. As the Galaxy evolves, the D/H abundance in the interstellar medium (ISM) decreases from its primordial value due to astration. However, the observed gas-phase D/H abundances of some sightlines in the local Galactic ISM are substantially lower than the expected reduction by astration. The missing D could have been depleted onto polycyclic aromatic hydrocarbon (PAH) molecules which are ubiquitous and abundant in interstellar regions. To quantitatively explore the hypothesis of PAHs as a possible reservoir of interstellar D, we quantum-chemically compute the infrared vibrational spectra of monodeuterated PAHs and their cations.We find that, as expected, when H in PAHs is replaced by D, the C-H stretching and bending modes at 3.3, 8.6, and 11.3 μm shift to longer wavelengths at ∼4.4, 11.4, and 15.4 μm, respectively, by a factor of ∼ √13/7, the difference in reduced mass between the C-H and C-D oscillators. From the computed spectra we derive the mean intrinsic band strengths of the 3.3 μm C-H stretch and 4.4 μm C-D stretch to be ⟨A3.3 ⟩ ≈ 13.2 km mol-1 and ⟨A4.4 ⟩ ≈ 7.3 km mol-1 for neutral deuterated PAHs which would dominate the interstellar emission at 3.3 and 4.4 μm. By comparing the computationally derived mean band-strength ratio of ⟨A4.4/A3.3 ⟩ ≈ 0.56 for neutral PAHs with the mean ratio of the observed intensities of ⟨I4.4/I3.3 ⟩ ≈ 0.019, we find that the degree of deuteration (i.e., the fraction of peripheral atoms attached to C atoms in the form of D) is ∼2.4%, corresponding to a D enrichment of a factor of ∼1200 with respect to the interstellar D/H abundance.