The gas-phase atomic/molecular layer deposition (ALD/MLD) technique is strongly emerging as a viable approach to fabricate new exciting inorganic-organic hybrid thin-film materials. However, much less effort has been made to develop new precursors specifically intended for ALD/MLD; this applies to both the organic and inorganic precursors, and in the latter case in particular to transition metal precursors. Here we introduce copper bisdimethylaminopropoxide (Cu(dmap)2) as a promising transition metal precursor for ALD/MLD to be combined with a variety of organic precursors with different backbones and functional groups, i.e. hydroquinone (HQ), terephthalic acid (TPA), 4,4′-oxydianiline (ODA), p-phenylenediamine (PPDA) and 1,4-benzenedithiol (BDT). Hybrid Cu-organic thin films were obtained from all five organic precursors with appreciably high growth rates ranging from 1.0 to 2.6 Å per cycle. However, the Cu(dmap)2 + HQ process was found to yield hybrid Cu-organic films only at temperatures below 120 °C, while at higher temperatures metallic Cu films were obtained. The films were characterized by XRR, GIXRD, FTIR, Raman, XPS and UV-Vis spectroscopy.