Correct counting respects the stable order principle whereby the count terms are recited in a fixed order every time. The 4 experiments reported here tested whether precounting infants recognize and prefer correct stable-ordered counting. The authors introduced a novel preference paradigm in which infants could freely press two buttons to activate videos of counting events. In the “correct” counting video, number words were always recited in the canonical order (“1, 2, 3, 4, 5, 6”). The “incorrect” counting video was identical except that the number words were recited in a random order (e.g., “5, 3, 1, 6, 4, 2”). In Experiment 1, 18-month-olds (n = 21), but not 15-month-olds (n = 24), significantly preferred to press the button that activated correct counting events. Experiment 2 revealed that English-learning 18-month-olds’ (n = 21) preference for stable-ordered counting disappeared when the counting was done in Japanese. By contrast, Experiment 3 showed that multilingual 18-month-olds (n = 24) preferred correct stable-ordered counting in an unfamiliar foreign language. In Experiment 4, multilingual 18-month-olds (N = 21) showed no preference for stable-ordered alphabet sequences, ruling out some alternative explanations for the Experiment 3 results. Overall these findings are consistent with the idea that implicit recognition of the stable order principle of counting is acquired by 18 months of age, and that learning more than one language may accelerate infants’ understanding of abstract counting principles.