The M dwarf star Gliese 581 is believed to host four planets, including one (GJ 581d) near the habitable zone that could possibly support liquid water on its surface if it is a rocky planet. The detection of another habitable-zone planet-GJ 581g-is disputed, as its significance depends on the eccentricity assumed for d. Analyzing stellar activity using the Ha line, we measure a stellar rotation period of 130 +/- 2 days and a correlation for H alpha modulation with radial velocity. Correcting for activity greatly diminishes the signal of GJ 581d (to 1.5 standard deviations) while significantly boosting the signals of the other known super-Earth planets. GJ 581d does not exist, but is an artifact of stellar activity which, when incompletely corrected, causes the false detection of planet g.