That syllable onsets are present in all languages is widely regarded as axiomatic, and the preference for syllabifying consonants as onsets over codas is considered a linguistic universal. The Central Australian language Arrernte provides the strongest possible counterevidence to this universal, with phenomena generally used to determine syllabification suggesting that all consonants in Arrernte are syllabified as codas at the word level. Attempts to explain the Arrernte facts in terms of syllables with onsets either make the wrong predictions or require proposals that render the putative onset universal unfalsifiable.