A search for CS J=7−6 emission from the core of the galaxy IC342 was undertaken with the Caltech Submillimeter Observatory. At the line frequency of 342.883 GHz, the beamsize is 20″. An upper limit to TMBΔv of 0.4 K km s−1 was obtained. This upper limit can be compared directly to the CS J=3−2 integrated line flux (3.1 K km s−1; Mauersberger and Henkel 1989), because the beam used for that observation was similar (17″). The J=7−6 to J=3−2 line ratio limit is 0.13 with no correction for the slight difference in beamsize, and ≈ 0.15 with this correction included. Assuming Tkin = 70 K (Martin and Ho 1986), this leads to a density upper limit of about 5 × 105 cm−3 for this gas.