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 Φ0 = (8.7 ± 1.0stat ± 1.8sys) × 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.