Aims. The supernova remnant (SNR) complex CTB 37 is an interesting candidate for observations with very high energy (VHE) $γ$-ray telescopes such as HESS. In this region, three SNRs are seen. One of them is potentially associated with several molecular clouds, a circumstance that can be used to probe the acceleration of hadronic cosmic rays. Methods. This region was observed with the HESS Cherenkov telescopes and the data were analyzed with standard HESS procedures. Recent X-ray observations with Chandra and XMM-Newton were used to search for X-ray counterparts. Results. The discovery of a new VHE $γ$-ray source HESS J1714-385 coincident with the remnant CTB 37A is reported. The energy spectrum is well described by a power-law with a photon index of $Γ$ = 2.30 $±$ 0.13 and a differential flux at 1 TeV of $Φ_0 = (8.7 ± 1.0_{\mathrm{stat}} ± 1.8_{\mathrm{sys}}) \times 10^{-13}$ cm-2 s-1 TeV-1. The integrated flux above 1 TeV is equivalent to 3% of the flux of the Crab nebula above the same energy. This VHE $γ$-ray source is a counterpart candidate for the unidentified EGRET source 3EG J1714-3857. The observed VHE emission is consistent with the molecular gas distribution around CTB 37A; a close match is expected in a hadronic scenario for $γ$-ray production. The X-ray observations reveal the presence of thermal X-rays from the NE part of the SNR. In the NW part of the remnant, an extended non-thermal X-ray source, CXOU J171419.8-383023, is discovered as well. Possible connections of the X-ray emission to the newly found VHE source are discussed. ; The support of the Namibian authorities and of the University of Namibia in facilitating the construction and operation of HESS is gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), the Max Planck Society, the French Ministry for Research, the CNRS-IN2P3 and the Astroparticle Interdisciplinary Programme of the CNRS, the UK Science and Technology Facilities Council (STFC), the IPNP of the Charles University, the Polish Ministry of Science and Higher Education, the South African Department of Science and Technology and National Research Foundation, and by the University of Namibia. We appreciate the excellent work of the technical support staff in Berlin, Durham, Hamburg, Heidelberg, Palaiseau, Paris, Saclay, and in Namibia in the construction and operation of the equipment. We wish to thank Estela Reynoso and Jeffrey Mangum for providing us their CO maps ; 53530