In the faint star KIC 9700322 observed by the Kepler satellite, 76 frequencies with amplitudes from 14 to 29 000 ppm were detected. The two dominant frequencies at 9.79 and 12.57 d-1 (113.3 and 145.5 μHz), interpreted to be radial modes, are accompanied by a large number of combination frequencies. A small additional modulation with a 0.16 d-1 frequency is also seen; this is interpreted to be the rotation frequency of the star. The corresponding prediction of slow rotation is confirmed by a spectrum from which v sin i= 19 ± 1 km s-1 is obtained. The analysis of the spectrum shows that the star is one of the coolest δ Sct variables. We also determine Teff = 6700 ± 100 K and log g = 3.7 ± 0.1, compatible with the observed frequencies of the radial modes. Normal solar abundances are found. An ℓ= 2 frequency quintuplet is also detected with a frequency separation consistent with predictions from the measured rotation rate. A remarkable result is the absence of additional independent frequencies down to an amplitude limit near 14 ppm, suggesting that the star is stable against most forms of non-radial pulsation. A low-frequency peak at 2.7763 d-1 in KIC 9700322 is the frequency difference between the two dominant modes and is repeated over and over in various frequency combinations involving the two dominant modes. The relative phases of the combination frequencies show a strong correlation with frequency, but the physical significance of this result is not clear. Based on observations obtained with the Hobby-Eberly Telescope, which is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München and Georg-August-Universität Göttingen.