We report on the first simultaneous near-infrared/X-ray detection of the Sgr A* counterpart which is associated with the massive black hole at the center of the Milky Way. The observations have been carried out using the NACO adaptive optics (AO) instrument at the European Southern Observatorys Very Large Telescope and the ACIS-I instrument aboard the Chandra X-ray Observatory. We also report on quasi-simultaneous observations at a wavelength of 3.4 mm using the Berkeley-Illinois-Maryland Association (BIMA) array. A flare was detected in the X-domain with an excess 2-8 keV luminosity of about 6$times10^{33}$ erg/s. A fading flare of Sgr A* with $>$2 times the interim-quiescent flux was also detected at the beginning of the NIR observations, that overlapped with the fading part of the X-ray flare. Compared to 8-9 hours before the NIR/X-ray flare we detected a marginally significant increase in the millimeter flux density of Sgr A* during measurements about 7-9 hours afterwards. We find that the flaring state can be conveniently explained with a synchrotron self-Compton model involving up-scattered sub-millimeter photons from a compact source component, possibly with modest bulk relativistic motion. The size of that component is assumed to be of the order of a few times the Schwarzschild radius. The overall spectral indices $alpha_{NIR/X-ray}$ ($S_{ u}$$propto$$ u^{-alpha}$) of both states are quite comparable with a value of $sim$1.3. Since the interim-quiescent X-ray emission is spatially extended, the spectral index for the interim-quiescent state is probably only a lower limit for the compact source Sgr A*. A conservative estimate of the upper limit of the time lag between the ends of the NIR and X-ray flare is of the order of 15 minutes.
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