Measurements of the microwave absorption spectrum of pairs of (J = 1) H2 molecules at low concentration in (J = 0) solid hydrogen in the frequency ranges 10–26 and 60–90 GHz are reported. Observation of absorptions with coefficients 10−5 cm−1 is accomplished by a novel calorimetric method. These absorptions result from transitions between energy levels of near neighboring pairs of (J = 1) molecules and assignments are made on the basis of selection rules, relative intensities, temperature dependences, and time evolution due to migration of (J = 1) molecules. Clustering of in-plane and of out-of-plane nearest neighbor pairs are observed to have time constants of 100 and 10 h, at 1.2 K and with 0.2% concentration of (J = 1) species. Peak frequencies, widths, and line shapes are determined with a resolution typically of order 5 to 50 MHz. Comparison is made to theoretical expressions for the transition frequencies, developed in the following paper, and several anisotropic potential parameters are determined, namely: the effective quadrupole coupling constant [Formula: see text], non-quadrupolar coupling constants ε0 = −1.55 × 10−2 cm−1 and ε2 = 1.1 × 10−2 cm−1, the crystal field Vc = 9.8 × 10−3 cm−1, and the difference in the quadrupole coupling for in- and out-of-plane nearest neighbor pairs ΔΓ/Γ = −1.4 × 10−3. The intensities of the observed transitions agree reasonably well with those calculated assuming a quadrupole-induced-dipole absorption process and using known values of the polarizability tensor of the H2 molecule. At low (J = 1) concentrations, the line widths are generally caused by inhomogeneous variations in Γ. At higher concentrations, the line widths agree qualitatively with the theory of Fujio, Hama, and Nakamura for spectral width due to longer range quadrupole interactions, although the line shapes do not correspond very well. Tentative assignments of transitions from further than nearest neighbor pairs are proposed.