The Bears have already been to five Super Bowls, including two in the past five years.
The Bears went to six in 2016, including a win over the Patriots in Super Bowl XLVII.
Cal is coming off a 9-7 season.
The Cardinal finished the season with the best record in the nation, finishing the season in the top 10.
It was the first time the Cardinal had won back-to-back Pac-12 titles since 2005.