The Cubs stole six bases on June 3. Since 1956, it is just the 5th time they've done it in a regulation game. None of these teams got caught in the process, except tonight's, as Ronny Cedeno got caught once after over sliding the base. He must have thought it was a walk. Other than that one play, the Cubs ran at will against former teammate, Michael Barrett.
The last Cubs team to do it was Don Baylor's 2000 club on May 14. The Cubs were visiting Montreal and got beat 16-15. Sammy Sosa had five hits and five RBI, but he wasn't the hitting star. Henry Rodriguez had four hits and seven RBI. Shane Andrews had one of the swipes, and it was the only one of the year, and the last of his career. The other five all belonged to Eric Young. Only one base was stolen off starter Hideki Irabu, so we can only blame Chris Widger for EY's follies.
The 1985 Cubs pulled it off twice. Bob Dernier had a pair in each game, and Ryne Sandberg had one each. Three Cubs stole over 30 bases in 1985 for Jim Frey, including Davey Lopes, who had two in the May game. Davey had just turned 40, but continued to run well through 1986, and retired in 1987.
In the 1970 game, Ron Santo and Billy Williams each stole two bases. This was an odd day for that club, since Leo's crew finished last in the National League with just 39 swipes. Don Kessinger's 12 (including one in this game) led the club. For comparison, the 1985 club was 2nd in the league with 182 steals, and the 2000 team managed 93 and finished 10th out of 16 teams. Not including tonight's games, the '08 Cubs are 9th in the league.
You can find all this stuff and more at baseball-reference.com. The Play Index goes much further back for individual players, but back to 1956 for game log searches is pretty good, I say.