2019 Update:
MLB will announce the MVP winners on November 14, 2019.
Cubs won't have any MVP winners in 2019, but Kris Bryant, Javier Baez & Anthony Rizzo all ended the season with a WAR of over 4 which should mean that at least one, if not all 3 may end up getting votes that put them in the top 20.
1911 NL MVP-Frank "Wildfire" Schulte
Schulte led the NL in Home Runs (21), RBI (107), Slg % (.534) & OPS+ (156)
November 18, 1987
Andre Dawson named NL Most Valuable Player
November 13, 1984
Ryne Sandberg is named NL MVP. For the season, Sandberg was an all-star, won the gold glove and silver slugger awards at 2B. He led the NL in runs scored (119) and triples (19) and finished 2nd in total hits (200). His efforts helped the Cubs make the playoffs and just one win short of a World Series appearance.
Chicago Cubs Most Valuable Player Award Winners
1911 Frank "Wildfire" Schulte
1929 Rogers Hornsby
1935 Gabby Hartnett
1945 Phil Cavaretta
1952 Hank Sauer
1958 Ernie Banks
1959 Ernie Banks
1984 Ryne Sandberg
1987 Andre Dawson
1998 Sammy Sosa
2016 Kris Bryant
Bryant won the Rookie of the Year award in 2015. He becomes the first Cubs player to win both Rookie of the Year and MVP. He's the 4th MLB player of all time to win Rookie of the Year and MVP in their first 2 seasons.
Ryne SandbergRecent Results:
Javier Baez finished 2nd in MVP voting in 2018
Anthony Rizzo finished 17th in MVP voting in 2018
Kris Bryant finished 7th in MVP voting in 2017
Anthony Rizzo finished 13th in MVP voting in 2017
Anthony Rizzo finished 4th in the NL MVP voting in 2016
Anthony Rizzo finished 4th in the NL MVP voting in 2015
Jake Arrieta finished 6th in the NL MVP voting in 2015
Anthony Rizzo finished 10th in the NL MVP voting in 2014
Derrek Lee finished 9th in the NL MVP voting in 2009
Aramis Ramirez finished 10th in the NL MVP voting in 2008
Derrek Lee finished 3rd in the NL MVP voting in 2005
Hall of Fame Cubs, No MVP's
A few Cubs that had Hall of Fame careers, but never won the MVP include Billy Williams, Ron Santo and Fergie Jenkins. Although, all 3 came very close a few years.
Fergie Jenkins was 7th in 1971. Fergie did take home the Cy Young award in 1971
Ron Santo had solid showings in the MVP race in both 1967 and 1969 finishing 4th in the voting in 1967 and 5th in the voting in 1969
It seems rather fitting that the low key go about his job type of player like Billy Williams came ever so close to taking home MVP honors in both 1970 and 1972 finishing second both years to eventual Hall of Fame catcher, Johnny Bench.