We report first results of a multifrequency campaign from radio to hard X-ray energies of the prominent gamma-ray blazar 3C 279, which was organised around an INTEGRAL ToO observation in January 2006, and triggered on its optical state. The variable blazar was observed at an intermediate optical state, and a well-covered multifrequency spectrum from radio to hard X-ray energies could be derived. The SED shows the typical two-hump shape, the signature of non-thermal synchrotron and inverse-Compton (IC) emission from a relativistic jet. By the significant exposure times of INTEGRAL and Chandra, the IC spectrum (0.3 - 100 keV) was most accurately measured, showing - for the first time - a possible bending. A comparison of this 2006 SED to the one observed in 2003, also centered on an INTEGRAL observation, during an optical low-state, reveals the surprising fact that - despite a significant change at the high-energy synchrotron emission (near-IR/optical/UV) - the rest of the SED remains unchanged. In particular, the low-energy IC emission (X- and hard X-ray energies) remains the same as in 2003, proving that the two emission components do not vary simultaneously, and provides strong constraints on the modelling of the overall emission of 3C 279.