Charge transport across metal-molecule interfaces has an important role in organic electronics(1). Typically, chemical link groups such as thiols(2) or amines(3) are used to bind organic molecules to metal electrodes in single-molecule circuits, with these groups controlling both the physical structure and the electronic coupling at the interface. Direct metal-carbon coupling has been shown through C60, benzene and p-stacked benzene(4-7), but ideally the carbon backbone of the molecule should be covalently bonded to the electrode without intervening link groups. Here, we demonstrate a method to create junctions with such contacts. Trimethyl tin (SnMe(3))-terminated polymethylene chains are used to form single-molecule junctions with a break-junction technique(2,3). Gold atoms at the electrode displace the SnMe(3) linkers, leading to the formation of direct Au-C bonded single-molecule junctions with a conductance that is similar to 100 times larger than analogous alkanes with most other terminations. The conductance of these Au-C bonded alkanes decreases exponentially with molecular length, with a decay constant of 0.97 per methylene, consistent with a non-resonant transport mechanism. Control experiments and ab initio calculations show that high conductances are achieved because a covalent Au-C sigma (sigma) bond is formed. This offers a new method for making reproducible and highly conducting metal-organic contacts.