Doppler spectroscopy of \rho ^ { 1 } Cnc has detected evidence of a companion with an orbital period of 14.65 days and a minimum mass of 0.88 Jupiter masses . Astrometric observations performed with the Hubble Space Telescope Fine Guidance Sensor 1r using a novel new observing technique have placed an upper limit on the astrometric reflex motion of \rho ^ { 1 } Cnc in a time period of only one month . These observations detected no reflex motion induced by the 14.65 day period radial velocity companion , allowing us to place a 3 \sigma upper limit of \sim 0.3 milliarcseconds on the semi-major axis of this motion , ruling out the preliminary Hipparcos value of 1.15 milliarcseconds . The corresponding upper limit on the true mass of the companion is \sim 30 M _ { J } , confirming that it is a sub-stellar object .