First mentions of chairmen I can find:
1909 - Chairman: Alderman Prevost
1910 - Chairman: R.A Jones
https://en.wikipedia.org/wiki/R._A._Jones
1913 - Chairman: George Radford (personally bankrolled the team to stop it going bust)
1919 - Chairman: WJ Kirby
1924 - Chairman: DeForest Morehouse (owner of the Kursaal)
1934 - Chairman: C.N Newitt (awarded the George Cross in WW2)
1952 - Chairman: Major Hay
1953 - Chairman: Alderman H H Smith
1957 - Chairman: Arthur Bewes (sadly died after just taking over, becoming ill during the tour to Czechoslovakia)
1958 - Chairman: Major Hay (who also took over manager duties after Eddie Perry left, signing Billy Wall and Peter Corthine, and after Frank Broome was sacked, also took over as manager)
1959 - Chairman: Alderman H H Smith
1960: Chairman (and manager, see above): Major Hay (who was now getting criticism from the fans, and responded, calling them "beatniks". Fans boycotted a game in 1961/2 and only 4,754 turned up, the lowest attendance at Roots Hall)
1969 - Chairman: Bill Rubin
1980 - Chairman: Frank Walton
1983 - Owner: Anton Johnson bought 44.9% the from Bill Rubin's sons, Mark and Tony. Andrew MacHutcheon was a "puppet" chairman. Bobby Moore was also Chief Executive.
October 1984: Anton Johnson was arrested and a new regime led by Vic Jobson took over
1985 - Vic announces a new £14m stadium
1998 - Chairman: John Main
1998 - Owner: Ron Martin, and chairman since 2000
There are gaps obviously, so any edits welcome...