We monitored the chromospheric activity in the Ca II H and K lines of 13 solar-type stars (including the Sun): 8 of them over 3 years at the Canada-France-Hawaii Telescope (CFHT) and 5 in a single run at the Very Large Telescope (VLT). A total of 10 of the 13 targets have close planetary companions. All of the stars observed at the CFHT show long-term (months to years) changes in H and K intensity levels. Four stars display short-term (days) cyclical activity. For two, HD 73256 and Kappa super(1) Cet, the activity is likely associated with an active region rotating with the star; however, the flaring in excess of the rotational modulation may be associated with a hot Jupiter. A planetary companion remains a possibility for Kappa super(1) Cet. For the other two, HD 179949 and upsilon And, the cyclic variation is synchronized to the hot Jupiter's orbit. For both stars this synchronicity with the orbit is clearly seen in two out of three epochs. The effect is only marginal in the third epoch at which the seasonal level of chromospheric activity had changed for both stars. Short-term chromospheric activity appears weakly dependent on the mean K line reversal intensities for the sample of 13 stars. In addition, a suggestive correlation exists between this activity and the M sub(p) sin i of the star's hot Jupiter. Because of their small separation ( less than or equal to 0.1 AU), many of the hot Jupiters lie within the Alfven radius of their host stars, which allows a direct magnetic interaction with the stellar surface. We discuss the conditions under which a planet's magnetic field might induce activity on the stellar surface and why no such effect was seen for the prime candidate, tau Boo. This work opens up the possibility of characterizing planet-star interactions, with implications for extrasolar planet magnetic fields and the energy contribution to stellar atmospheres.