Housed in a rare example of a late-medieval Welsh town house, the Owain Glyndŵr Centre houses an exhibition telling the story of the Welsh hero's fight for independence and starring the Pennal letter, written by Glyndŵr in pursuit of an alliance with the French. Although it's called the Old Parliament Building, it was probably built around 1460, some 50 years after Glyndŵr instituted his parliament on this site, but it's believed to closely resemble the former venue.
If it's locked, ask for the key at the Caffi Alys next door.
