As of this second, the Chicago Bears have $27,615,288 in available cap space according to the National Football League Players Association. The NFLPA updates their list daily, and they only count the top 51 paid players on a roster in their calculations.
The "rule of 51" only applies to the offseason, and once the season starts the entire roster will count towards the cap. The active 53 man roster, the practice squad, the physically unable to perform list and even those on injured reserve will count towards the 2016 cap. As of right now the Bears have 66 players on their roster, and offseason rules allow them to carry 90 players.
Chicago's $27,615,288 in cap space actually places them 5th most in the NFL. Tops is the San Francisco 49ers at $59,190,891, followed by the Jacksonville Jaguars at $57,288,257. The Cleveland Browns have the 3rd most at $42,718,501, with the Tennessee Titans in 4th at $35,795,847.
The Pittsburgh Steelers have the least amount of cap space at $2,629,520, followed by the New York Jets at $2,909,647 and the Arizona Cardinals at $3,974,926.
For the full list of cap space you can click here.