First published as pre-print arXiv:0711.2491v1 (11/15/2007), then published in Physical Review Letters 99, 10 106101 (2007)Using low energy electron microscopy we observe that Pd deposited on Ru only attaches to small sections of the atomic step edges surrounding Pd islands. This causes a novel epitaxial growth mode in which islands advance in a snakelike motion, giving rise to labyrinthine patterns. Based on density functional theory together with scanning tunneling microscopy and low energy electron microscopy we propose that this growth mode is caused by a surface alloy forming around growing islands. This alloy gradually reduces step attachment rates, resulting in an instability that favors adatom attachment at fast advancing step sections.This research was partly supported by the Office of Basic Energy Sciences, Division of Materials Sciences, U.S. Department of Energy under Contracts No. DE-AC04-94AL85000 and No. DE-AC02-05CH11231, and by the Spanish Ministry of Science and Technology through Project No. MAT2006-13149-C02-02.Peer reviewed