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The G0 V star HD 166435 has been observed by the fiber-fed spectrograph ELODIE as one of the targets in the large extra-solar planet survey that we are conducting at the Observatory of Haute-Provence. We detected coherent, low-amplitude, radial-velocity variations with a period of 3.7987 days, suggesting a possible close-in planetary companion. Subsequently, we initiated a series of high-precision photometric observations to search for possible planetary transits and an additional series of Ca II H and K observations to measure the level of surface magnetic activity and to look for possible rotational modulation. Surprisingly, we found the star to be photometrically variable and magnetically active. A detailed study of the phase stability of the radial-velocity signal revealed that the radial-velocity variability remains coherent only for durations of about 30 days. Analysis of the time variation of the spectroscopic line profiles using line bisectors revealed a correlation between radial velocity and line-bisector orientation. All of these observations, along with a one-quarter cycle phase shift between the photometric and the radial-velocity variations, are well explained by the presence of dark photospheric spots on HD 166435. We conclude that the radial-velocity variations are not due to gravitational interaction with an orbiting planet but, instead, originate from line-profile changes stemming from star spots on the surface of the star. The quasi-coherence of the radial-velocity signal over more than two years, which allowed a fair fit with a binary model, makes the stability of this star unusual among other active stars. It suggests a stable magnetic field orientation where spots are always generated at about the same location on the surface of the star.