The story
First attested mid-16th century. Origin obscure. Possibly from *gibber, of onomatopoeic origin imitating to the sound of chatter, possibly from or influenced by jabber, + -ish denoting the name of a language (compare English, Finnish, Spanish, etc.). The verb gibber, first attested circa 1600, is usually regarded as a back-formation from gibberish.
Etymology from Wiktionary, CC BY-SA 4.0.