The rapidly varying non-thermal X-ray emission observed from Sgr A* points to particle acceleration taking place close to the supermassive black hole. The TeV gamma -ray source HESS J1745-290 is coincident with Sgr A* and may be closely related to the X-ray emission. Simultaneous X-ray and TeV observations are required to elucidate the relationship between these two objects. Here we report on joint H.E.S.S./Chandra observations in July 2005, during which an X-ray flare was detected. Despite a factor >10 increase in the X-ray flux of Sgr A*, no evidence is found for an increase in the TeV gamma -ray flux. We find that an increase of the gamma -ray flux of a factor 2 or greater can be excluded at a confidence level of 99%. This finding disfavours scenarios in which the bulk of the gamma -ray emission observed is produced close to Sgr A*.