He finished the 2006 Chicago Bears season as a clutch performer on the Bears' defense. Briggs was selected to play in the 2007 Pro Bowl, but opted to decline the invitation because of an injured foot. He became a free agent following the 2007 playoffs, leaving his future with the Bears in the air. Despite Briggs’ high price tag, commentary from NFL on Fox revealed Brian Urlacher was willing to take a pay-cut in order to keep Briggs on the team. On February 16, 2007, the Bears officially placed the franchise tag on him, which guarantees him a one-year contract for the 2007 NFL season at slightly more than $7.2 million.
On March 12, 2007, Briggs announced that he no longer considered himself a member of the Chicago Bears. During a cell phone interview with Foxsports.com Briggs said "I am now prepared to sit out the year if the Bears don't trade me or release me, I've played my last snap for them. I'll never play another down for Chicago again." In explaining his demands, he said "The Bears have shown I'm not in their long-term plans so if that's the case, I don't want to be here." A report from Fox Sports on March 27 claimed that the Washington Redskins allegedly offered the Bears their first round pick in exchange for Briggs and the Bears' own first round pick. On March 28, Bears general manager Jerry Angelo confirmed that the Redskins have made a trade offer and stated, "We'll evaluate if that's good for us and get back to them". Angelo rejected the offer on April 3, but later stated they were interested in negotiating a deal the following day. The Bears then proposed a trade with the Redskins which included linebacker Rocky McIntosh as well as the Redskins first-round pick in exchange for Briggs. Briggs did not attend the team's first meeting after their Super Bowl XLI loss, or their mandatory mini camp session in May 2007. Despite his comments, the Bears re-signed Briggs to a six-year, $36 million contract on March 1, 2008.
In August 2007, Briggs crashed his new Lamborghini Murcielago into a light pole. He then left the scene of the accident and reported his car stolen. He was charged with leaving the scene of an accident. He was also cited for failure to give immediate notice of an accident and improper lane usage.