This Letter reports the discovery of a remarkably hard spectrum source, HESS J1641-463, by the High Energy Stereoscopic System (H.E.S.S.) in the very high energy (VHE) domain. HESS J1641-463 remained unnoticed by the usual analysis techniques due to confusion with the bright nearby source HESS J1640-465. It emerged at a significance level of 8.5 standard deviations after restricting the analysis to events with energies above 4 TeV. It shows a moderate flux level of varphi(E > 1 TeV) = (3.64 0.44 sub(stat) 0.73 sub(sys)) x 10 super(-13) cm super(-2) s super(-1), corresponding to 1.8% of the Crab Nebula flux above the same energy, and a hard spectrum with a photon index of Gamma = 2.07 0.1l sub(stat) 0.20 sub(sys). It is a point-like source, although an extension up to a Gaussian width of sigma = 3 arcmin cannot be discounted due to uncertainties in the H.E.S.S. point-spread function. The VHE gamma-ray flux of HESS J1641-463 is found to be constant over the observed period when checking time binnings from the year-by-year to the 28 minute exposure timescales. HESS J1641-463 is positionally coincident with the radio supernova remnant SNR G338.5+0.1. No X-ray candidate stands out as a clear association; however, Chandra and XMM-Newton data reveal some potential weak counterparts. Various VHE gamma-ray production scenarios are discussed. If the emission from HESS J1641-463 is produced by cosmic ray protons colliding with the ambient gas, then their spectrum must extend close to 1 PeV. This object may represent a source population contributing significantly to the galactic cosmic ray flux around the knee.