We report a strong compression of space around a visual anchor presented in the near visual periphery (<5°). While subjects kept fixation, a salient visual stimulus (from now on referred to as "anchor") was presented, followed by a brief whole-field mask. At various times around mask onset a probe dot was flashed. Subjects estimated the position of the probe dot in relation to a subsequently presented comparison bar. The probe dot location was perceived nearly veridically when presented long before or after mask onset. However, when the probe dot was presented simultaneously with the mask it appeared shifted toward the anchor by as much as 50% of their separation. The anchor had to appear briefly before mask onset to attract the probe dot. No compression occurred when the anchor was presented long before or after the mask. When the probe dot and anchor were presented with similar brief duration, the more peripheral stimulus always shifted toward the more foveal stimulus independently of their temporal order. We hypothesize that the attraction might be explained by the summation of the neural activity distributions of probe and anchor.