The name of the street comes from the Chichester family, landlords of Belfast from 1603, when lands were granted to Sir Arthur Chichester by James I, shortly before appointing him as Lord Deputy of Ireland. Chichester built a castle at Belfast in 1611, roughly where Castle Place and Castle Street are today. The family was from North Devon. The head of this family has held the title Earl of Donegall and later Marquess of Donegall from the 17th to the present, but the 2nd Marquess ceased to be a significant Belfast landlord, selling much of his property from the 1820s onwards to repay debts.
Chichester Avenue features in The Belfast and Province of Ulster Directory (1884).
The Irish form of the name was approved in July 2023.