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 compute quantumchemically the infrared vibrational spectra of mono-deuterated 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. We derive from the computed spectra the mean intrinsic band strengths of the 3.3 µm C-H stretch and 4.4 µm C-D stretch to be A 3.3 ≈ 13.2 km mol −1 and A 4.4 ≈ 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 A 4.4 /A 3.3 ≈ 0.56 for neutral PAHs with the mean ratio of the observed intensities of I 4.4 /I 3.3 ≈ 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.