From Middle English pultrie, from Old French pouleterie, from poulet, diminutive of poule (“hen”), from Latin pullus (“chick”). By surface analysis, poult + -ry. For the development of Middle English /u/ to modern /oʊ/, /əʊ/ before /lt/, /ld/, /ln/, compare boult, boulder, colter/coulter, poultice, shoulder, won't.