We have observed an anomalous broadening of the NMR absorption line of diluted ortho-H z (with rotational angular momentum J :-1) in solid para-H 2 (J = O) as pressure is applied. Samples with 0.015 < x < 0.06, where x is the ortho mole fraction, were studied over the temperature range 1.2 < T < 4.2 K. The density range covered was Po < P < 1.7po, Po being the density at zero pressure. The observed broadening was much larger than that estimated from intermolecular and intramolecular nuclear dipolar interaction, the latter resulting from short-range orientational molecular ordering caused by electric quadrupole-quadrupole (EQQ) interactions. Furthermore, the "average" longitudinal relaxation time T~ measured from the initial nuclear magnetization recovery after saturation is found to decrease with increasing density, contrary to what is predicted from the relaxation mechanism based on EQQ interaction. Arguments based on NMR measurements taken in solid Dz show that any orientational ordering of the J = 0 molecules caused by an admixture of J = 2 states is too small to lead to polarization of the J = 1 molecules large enough to account for the anomalous line shape. Another possible explanation of the anomaly--rapid clustering of the J = 1 impurities--is also Jound to be unlikely. The anomalously broadened line, with a width proportional to T-1 gt a given density, is discussed in terms of local molecular alignment of the 'J = 1 impurities as produced by a crystalline field V c and that causes an increase In the intramolecular dipolar feld. From the NMR line shape, we can get information on the distribution of such fields throughout the lattice. A crude analysis indicates that the distribution is approximately Gaussian around a characteristic value V,/k e where the width of this distribution is of the order of Vc/k B. At p = 1.7po, [V,l/k n is found to have a value of ~0.6 K, which is about 30 times larger than previous determinations at p = Po. The origins of the anomalously large crystalline field are discussed.