It has long been speculated that the observed periodic radial velocity pattern for the K giant Pollux might be explained in terms of an orbiting planetary companion. We have collected 80 high-resolution spectra for Pollux at Lick Observatory yielding precise radial velocities with a mean error of 3.8 m s-1, providing the most comprehensive and precise data set available for this star. Our data confirm the periodicity previously seen in the radial velocities. We derive a period of 589.7 ± 3.5 days and, assuming a primary mass of 1.86 M, a minimum companion mass of 2.9 ± 0.3MJup, consistent with earlier determinations. No evidence for any periodicities is visible in our analysis of the shapes of the spectral lines via the bisector method, so we conclude that evidence is accumulating and compelling for a planet around Pollux. However, some final doubt remains about this interpretation, because nonradial pulsations that might be present in giant stars could in principle also explain the observed radial velocities, while the accompanying bisector variations might be too small to be detectable with current data.