The rapidly varying ( 10 minute timescale) non-thermal X-ray emission observed from Sgr A* implies that particle acceleration is occuring close to the event horizon of the supermassive black hole. The TeV gamma -ray source HESS J1745-290 is coincident with Sgr A* and may be closely related to its X-ray emission. Simultaneous X-ray and TeV observations are required to elucidate the relationship between these objects. We report on joint H.E.S.S./Chandra observations performed in July 2005, during which an X-ray flare was detected. Despite a factor of 9 increase in the X-ray flux of Sgr A*, no evidence is found for an increase in the TeV gamma -ray flux from this region. We find that an increase in the gamma -ray flux of a factor of 2 or greater can be excluded at a confidence level of 99%. This finding disfavours scenarios in which the keV and TeV emission are associated with the same population of accelerated particles and in which the bulk of the gamma -ray emission is produced within 1014 cm ( 100 R_S) of the supermassive black hole.