This article argues that piyyut (Hebrew liturgical poetry) bears the structural form of a destabilizing supplement to prayer, not only in its earliest stages but also in later eras of worship and culture, and that reading both prayer and poem through the notion of supplementarity reveals their generous and risky contribution to worship. It is well known that ancient piyyut replaced parts of the prayer or was added to it, but the liturgical and poetic implications of this fact have barely been discussed. One such implication has to do with destabilization in various forms that are inherent to the curious position of the supplement. It was Jacques Derrida who first explored the dangerous riches of supplementarity and its “illogical logic,” and some of his central observations serve here as guiding lights to a new understanding of the relation between prayer and poetry in the synagogue. The first part of the article introduces this view of piyyut through a critique of the prevalent scholarly accounts of piyyut as poetry and prayer and a close reading of two short medieval piyyutim. The second part of the article offers a close supplemental reading of one tenth-or early eleventh-century piyyut, taking note of its liturgical context and its destabilizing position within the fixed prayer.