Using the 100-m Green Bank Telescope, we have conducted a cm-wavelength search for CO J = 1-0 line emission towards the high-redshift, far-infrared (FIR) luminous object HDF850.1 over the redshift interval 3.3 less than or similar to z less than or similar to 5.4. Despite the wealth of existing multiwavelength observations, and the recent identification of a galaxy counterpart in deep K'-band (2.2 mu m) imaging, an unambiguous spectroscopic redshift has not yet been obtained for this object. A FIR-to-radio wavelength photometric redshift technique, however, predicts a similar to 90 per cent probability that the redshift is in the range, 3.3 less than or similar to z less than or similar to 5.4 (equivalent to an observed redshifted CO J= 1-0 emission line frequency, 26.5 greater than or similar to nu(obs) greater than or similar to 18.0 GHz), making HDF850.1 a potential occupant of the 'high-redshift tail' of submillimetre (submm)-selected galaxies. We have also conducted a search for CO J = 2-1 line emission over the narrower redshift range, 3.9 less than or similar to z less than or similar to 4.3. Although we do not detect any CO line emission in this object, our limits to the CO line luminosity are in broad agreement with the median value measured in the current sample of high-redshift, submm-selected objects detected in high-J CO line emission, but not sufficient to fully test the validity of the photometric redshift technique.