In order to complete the knowledge of the magnetic field and of its influence during the transition from Asymptotic Giant Branch to Planetary Nebulae stages, we have undertaken a search for magnetic fields at the surface of Mira stars. We used spectropolarimetric observations, collected with the Narval instrument at TBL, in order to detect - with Least Squares Deconvolution method - a Zeeman signature in the visible part of the spectrum. We present the first spectropolarimetric observations of the S-type Mira star chi Cyg, performed around its maximum light. We have detected a polarimetric signal in the Stokes V spectra and we have established its Zeeman origin. We claim that it is likely to be related to a weak magnetic field present at the photospheric level and in the lower part of the stellar atmosphere. We have estimated the strength of its longitudinal component to about 2-3 Gauss. This result favors a 1/r law for the variation of the magnetic field strength across the circumstellar envelope of chi Cyg. This is the first detection of a weak magnetic field at the stellar surface of a Mira star and we discuss its origin in the framework of shock waves periodically propagating throughout the atmosphere of these radially pulsating stars. At the date of our observations of chi Cyg, the shock wave reaches its maximum intensity, and it is likely that the shock amplifies a weak stellar magnetic field during its passage through the atmosphere. Without such an amplification by the shock, the magnetic field strength would have been certainly too low to be detected. For the first time, we also report strong Stokes Q and U signatures (linear polarization) centered onto the zero velocity (i.e., at the shock front position). They seem to indicate that the radial direction would be favored by the shock during its propagation throughout the atmosphere.< Leer menos