According to shirts being sold by Old Navy, the Houston Texans won the 1961 AFC championship.
Of course, neither the Houston Texans nor the AFC existed in 1961. A Houston team did win a championship that year, but it was the Oilers (who are now the Tennessee Titans), and it was the AFL championship. The AFL and NFL did not merge until 1970, at which point the league was divided into two conferences, the AFC and NFC.
A spokesman for Gap Inc., which owns Old Navy, told ESPN the shirts are made by a third-party sports licensing company and that the shirts are being removed.
The Texans made the first playoff appearance in franchise history last season, falling in the AFC Divisional round to the Baltimore Ravens.