。
She is a real chatterbox.
Literal
She [topic-は] great [genitive-の] talker is.
大の~ is an intensifier 'a great / huge X,' here applied to おしゃべり ('chatterbox / talkative person'). おしゃべり is built from お (prefix) + 喋り (the ます-stem of 喋る 'chat'); the お adds a softer, sometimes slightly affectionate or trivializing tone. ~である is the formal/written copula, more elevated than だ; the choice signals a stiffer, more written register that contrasts with the colloquial subject matter.