Before I get into these numbers, I should point out that none of these are official Cubs team records.
Rather, they are the best marks put up by Cubs players during any 60-game stretch in a single season during their Cubs careers. These numbers are all since 1901, and hat tip to Cubs historian Ed Hartig for the numbers.
Hits: 101, Kiki Cuyler (1930)
1930 was an offensive onslaught of a season. The entire National League hit .303 (!), and that included pitchers. Three Cubs (Cuyler, 228, Woody English, 214 and Hack Wilson, 208) had over 200 hits that year.