He was the son of Thomas Chichele of Higham Ferrers and Agnes Pyncheon, and the brother of Henry Chichele, the Archbishop of Canterbury and founder of All Souls College, Oxford. Another brother, William, also served as Sheriff of London in 1409.
Robert served as an alderman for Aldgate Ward from 1402, when he also served as Sheriff of London before being elected twice as Lord Mayor of London, in 1411 and again in 1421. He received letters patent ordering him (along with then-mayor Richard Whittington) to seek out and imprison any Lollards within the city. In 1414 and 1415 he was Member of Parliament for the City of London as one of the two aldermanic representatives.
- The Visitation of Cambridge, 1575 and 1619, by Henery St.George, Richmond Herald, edited by John W. Clay, F.S.A., Harleian Society, London, 1897, p.33.
- "Lord Mayors of the City of London from 1189" (PDF). www.citybridgetrust.gov.uk. Archived from the original (PDF) on 14 July 2014. Retrieved 9 June 2014.
- Burke, John, and Burke, Bernard "General Armory of England, Scotland, and Ireland"
- Riddy, Felicity "Prestige, Authority, and Power in Late Medieval Manuscripts and Texts" pg. 91
- "Chronological list of aldermen: 1302-1400". British History Online. Retrieved 7 October 2016.
- Newcourt, Richard (1708). Repetorium Ecclesiasticum Parochiale Londinense. 1. London. pp. 438–9.
- Cox, John Edmund "The Annals of St. Helen's, Bishopsgate, London" pg. 247