1560s, "in public," from public (adj.) + -ly (2). From 1580s as "by the public." Variant publically is attested from 1812, perhaps based on the fact that publicly is the only exception in this class of words, which as a rule are spelled -ically though often they are pronounced otherwise.
she admitted publicly to being a communist
publicly provided medical care
publicly financed schools
publicise
publicist
publicity
publicization
publicize
publicly
publish
publishable
publisher
publishing
puce