Final answer:
Sir Gawain meets the Green Knight for the second time at the Green Chapel, concluding his quest in the Arthurian chivalric romance.
Step-by-step explanation:
The place where Sir Gawain meets the Green Knight for the second time is the Green Chapel, which is a significant location in the narrative of the chivalric romance Sir Gawain and the Green Knight. This meeting is crucial as it concludes Sir Gawain's year-long quest to find the Green Knight and fulfill the terms of their agreement, which began with a challenge at King Arthur's court. The story of Sir Gawain is part of the Arthurian legends, marked by chivalric adventures set in medieval times.