This name was borne by the heroine of Lewis Carroll's novels Alice's Adventures in Wonderland (1865) and Through the Looking Glass (1871).
As an English name, Chloe has been in use since the Protestant Reformation. It started getting more popular in the 1980s in the United Kingdom and then the United States. It was the most popular name for girls in England and Wales from 1997 to 2002. This is one of the few English-language names that is often written with a diaeresis, as Chloë.
This name also appears in the New Testament, belonging to man who sheltered Paul and Silas. In his case, it may represent a Hellenized form of a Hebrew name. It was not used in England until after the Protestant Reformation.