Our understanding of galaxy evolution has traditionally been driven by pre-selection of galaxies based on their broad-band continuum emission. This approach is potentially biased, in particular against gas-rich systems at high-redshift which may be dust-obscured. To overcome this limitation, we have recently concluded a blind CO survey at 3mm in a region of the Hubble Deep Field North using the IRAM Plateau de Bure Interferometer. Our study resulted in 1) the discovery of the redshift of the bright SMG HDF850.1 (z = 5.183); 2) the discovery of a bright line identified as CO(2-1) arising from a BzK galaxy at z = 1.785, and of other 6 CO lines associated with various galaxies in the field; 3) the detection of a few lines (presumably CO(3-2) at z ~ 2) with no optical/NIR/MIR counterparts. These observational results allowed us to expand the parameter space of galaxy properties probed so far in high-z molecular gas studies. Most importantly, we could set first direct constraints on the cosmic evolution of the molecular gas content of the universe. The present study represents a first, fundamental step towards an unbiased census of molecular gas in `normal' galaxies at high-z, a crucial goal of extragalactic astronomy in the ALMA era.