Though Petrarch wrote his sonnets about his beloved Laura in Italian, he expected to be remembered for his Latin epic poems. In England during Chaucer's time, Latin was not so much the language of choice as was French. Since the Normans had ruled England for three hundred years, everyone who was anyone spoke and wrote in French. Chaucer's friend and rival, "moral Gower," wrote a treatise in Latin, the Vox Clamantis (circa 1379-1381), and one in French, the Mirour de l'Omme (circa 1376-1378), to match his great English work the Confessio Amantis (circa 1386). And so it was not at all assumed that an English writer would write in English, especially not someone in the odd personal circumstances of Chaucer.
Chaucer was probably quite comfortable with Latin since he translated Boethius's Consolation of Philosophy into English, and yet there is no reason to suspect that he did not have John Gower's fluency. For example, he often used French translations of Latin texts: the French Livre Griseldis instead of Petrarch's Latin version of the story of Griselda or the Ovide Moralise instead of the Latin Metamorphoses. Though his Latin was certainly better than that of William Shakespeare, whom Ben Jonson twitted about his small Latin and less Greek, it seems unlikely that he had the fluency even if he had the desire to write in Latin.