We report the existence of a previously unsuspected peak in the H-1 magic angle spinning spectrum of commercially available HZSM-5 samples. At 298 K, this resonance is a broad shoulder on the downfield side of the Bronsted acid signal at 4.3 ppm. Cooling the sample caused the line to narrow, and a clear peak at 6.9 ppm was visible at 123 K. As a first step in the assignment of this resonance, we report the results of several H-1{Al-27} double-resonance experiments in the context of the broad Al-27 resonance of the dehydrated zeolite, Reverse cross polarization (Al-27 --> H-1) failed as an assignment technique, but a related indirect detection experiment in which H-1 transverse magnetization was drained to Al-27 performed marginally better. A more successful experiment resembled H-1 observation with Al-27 decoupling; we call this experiment "quadrupole tickling", because the Al-27 irradiation was insufficient for true decoupling. This technique resulted in selective broadening of the 4.3 and 6.9 ppm resonances as a result of conflicting averaging of the H-1-Al-27 dipolar coupling. The silanol resonance was unaffected by this procedure, as expected for a proton environment remote from Al-27. Quadrupole tickling is shown to be related to a previously described spin-echo double resonance experiment. H-1 2D experiments were carried out on HZSM-5 with a variety of temperatures and mixing times. These show that site exchange between the 6.9 and 4.3 ppm resonances is negligible on the time scale of the double resonance experiments, but exchange occurs to a measurable extent at 250 ms. We conclude that the 6.9 ppm resonance corresponds to a novel aluminum-containing site in zeolite HZSM-5 and is not an artifact due to exchange with the Bronsted site or an aluminum-rich impurity phase. A possible interpretation of these results is a second Bronsted site for the zeolite.