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We present a molecular line scan in the Hubble Deep Field North (HDF-N) thatcovers the entire 3mm window (79-115 GHz) using the IRAM Plateau de BureInterferometer. Our CO redshift coverage spans z<0.45, 1<z<1.9 and all z>2. Wereach a CO detection limit that is deep enough to detect essentially all z>1 COlines reported in the literature so far. We have developed and applieddifferent line searching algorithms, resulting in the discovery of 17 linecandidates. We estimate that the rate of false positive line detections is~2/17. We identify optical/NIR counterparts from the deep ancillary database ofthe HDF-N for seven of these candidates and investigate their available SEDs.Two secure CO detections in our scan are identified with star-forming galaxiesat z=1.784 and at z=2.047. These galaxies have colors consistent with the `BzK'color selection and they show relatively bright CO emission compared withgalaxies of similar dust continuum luminosity. We also detect two spectrallines in the submillimeter galaxy HDF850.1 at z=5.183. We consider anadditional 9 line candidates as high quality. Our observations also provide adeep 3mm continuum map (1-sigma noise level = 8.6 $\mu$Jy/beam). Via a stackingapproach, we find that optical/MIR bright galaxies contribute only to <50% ofthe SFR density at 1<z<3, unless high dust temperatures are invoked. Thepresent study represents a first, fundamental step towards an unbiased censusof molecular gas in `normal' galaxies at high-z, a crucial goal ofextragalactic astronomy in the ALMA era.

A molecular line scan in the Hubble Deep Field North