In previous infant studies on statistics-based word segmentation, the unit of statistical computation was always aligned with the syllabic edge, which had a consonant onset. The current study addressed whether the learning system imposes a constraint that favors word forms beginning with a consonant onset over those beginning with an onsetless sub-syllable, by examining infants' segmentation of vowel-initial non-words in French liaison. French-learning 20- and 24-month-old infants ("N" = 64) were familiarized with sentences containing variable liaison consonants preceding the same vowel-initial non-word (e.g., /n/"onche", /z/"onche", /r/"onche", /t/"onche"), such that the distributional cues supported the sub-syllabic target (e.g., "onche"). After familiarization, we tested sub-syllabic statistical segmentation by presenting the vowel-initial target (e.g., "onche") versus another non-familiarized vowel-initial word (e.g., "èque"). Another group of infants was tested with a consonant-initial mis-segmentation of the target (e.g., "zonche") versus another non-familiarized consonant-initial word (e.g., "zèque"). Results showed that 20-month-olds failed to segment the vowel-initial targets, but they mis-segmented the targets as consonant-initial, indicating that the onset bias dominated over sub-syllabic statistics for word segmentation at this age. Twenty-four-month-olds showed ambiguous interpretations (i.e., both vowel-initial segmentation and consonant-initial mis-segmentation), suggesting that the use of statistics to segment sub-syllabic words was emerging while the onset bias continued to have an impact.