We report the results of our CO J = 4 → 3 line and rest-frame 650 μm continuum observations of the z = 0.93 hyperluminous infrared galaxy FSC 15307+3252 using the Owens Valley Millimeter Array. No line or continuum emission was detected, but the derived limits provide a useful constraint on the temperature, emissivity, and mass of the cold dust associated with FSC 15307+3252 and its molecular gas content. The 3 σ upper limit on the velocity-integrated CO (4-3) line flux is 1.6 Jy km s-1 (for ΔV = 300 km s-1). This corresponds to a surprisingly small total molecular gas mass limit of 5 × 109 h-2 M☉ for this galaxy with infrared luminosity LFIR > 1013 L☉. Combined with existing photometry data, our 3 σ upper limit of 5.1 mJy for the 239 GHz (650 μm rest wavelength) continuum flux yields a total dust mass of 0.4-1.5 times 108 M☉. The CO luminosity (thus molecular gas content) and the resulting gas-to-dust ratio are lower than the values typical for the more gas-rich infrared galaxies, but they are within the observed ranges. On the other hand, FSC 15307+3252 has a dust content and infrared luminosity 40 and 200 times larger than the infrared bright elliptical-like galaxies NGC 1275 and Cygnus A. The far-infrared (FIR) luminosity to dust mass ratios, LFIR/Mdust, for all three galaxies hosting a powerful active galactic nucleus (FSC 10214+4724, FSC 15307+3252, and Cygnus A) are larger than reasonably expected for a galaxy dominated by a starburst and 4 times larger than Arp 220. Therefore the bulk of the observed FIR luminosity in these galaxies is likely powered by their luminous active nuclei.