The discovery of very high energy (VHE) gamma-ray emitting X-ray binaries has triggered an intense effort to better understand the particle acceleration, absorption, and emission mechanisms in compact binary systems, which provide variable conditions along eccentric orbits. Despite this, the nature of some of these systems, and of the accelerated particles producing the VHE emission, is unclear. To answer some of these open questions, we conducted a multiwavelength campaign of the VHE gamma-ray emitting X-ray binary LS I +61 303 including the MAGIC telescope, XMM-Newton, and Swift during 60% of an orbit in 2007 September. We detect a simultaneous outburst at X-ray and VHE bands, with the peak at phase 0.62 and a similar shape at both wavelengths. A linear fit to the simultaneous X-ray/VHE pairs obtained during the outburst yields a correlation coefficient of r = 0.97, while a linear fit to all simultaneous pairs provides r = 0.81. Since a variable absorption of the VHE emission towards the observer is not expected for the data reported here, the correlation found indicates a simultaneity in the emission processes. Assuming that they are dominated by a single particle population, either hadronic or leptonic, the X-ray/VHE flux ratio favors leptonic models. This fact, together with the detected photon indices, suggests that in LS I +61 303 the X-rays are the result of synchrotron radiation of the same electrons that produce VHE emission as a result of inverse Compton scattering of stellar photons.