Context. The prominent blazar 3C 279 is known for its large-amplitude variability throughout the electromagnetic spectrum and its often γ-ray-dominated spectral energy distribution. However, the characterization of its broadband spectral variability still lacks a consistent picture, and the origin of its high-energy emission is still unclear. Aims. We intend to characterize the spectral energy distribution (SED) and spectral variability of 3C 279 in its optical high state. Methods. Prompted by an optical high state of 3C 279, we organized an extensive multiwavelength campaign with coverage from radio to hard X-ray energies. The core components of the campaign were INTEGRAL and Chandra ToO observations in January 2006, augmented by X-ray data from Swift and RXTE as well as radio through optical coverage. Results. The blazar was observed at a moderately high optical state. A well-covered multifrequency spectrum from radio to hard X-ray energies could be derived. During the flare, the radio spectrum was inverted, with a prominent spectral peak near 100 GHz, which propagated in time toward lower frequencies. The SED shows the typical two-bump shape, the signature of non-thermal emission from a relativistic jet. As a result of the long exposure times of INTEGRAL and Chandra, the high-energy spectrum (0.3−100 keV) was precisely measured, showing – for the first time – a possible downward curvature. A comparison of this SED from 2006 to the one observed in 2003, also centered on an INTEGRAL observation, but during an optical low-state, revealed the surprising fact that – despite a significant change of the high-frequency synchrotron emission (near-IR/optical/UV) – the low-energy end of the high-energy component (X-ray energies) remained virtually unchanged compared to 2003. Conclusions. Our results prove that the two emission components do not vary simultaneously. This provides strong constraints on the modeling of the overall emission of 3C 279. When interpreted with a steady-state leptonic model, the variability among the SEDs displaying almost identical X-ray spectra at low flux levels, but drastically different IR/optical/UV fluxes, can be reproduced by a change solely of the low-energy cutoff of the relativistic electron spectrum. In an internal shock model for blazar emission, such a change could be achieved through a varying relative Lorentz factor of colliding shells producing internal shocks in the jet, and/or the efficiency of generating turbulent magnetic fields (e.g., through the Weibel instability) needed for efficient energy transfer from protons to electrons behind the shock.