She's still chatting away.

Literal

She [topic-は] still chatter [object-を] is-doing.

おしゃべり is a noun meaning 'chat, gossip, chitchat,' and おしゃべりをする makes a light-verb construction ('do chatter' = 'chat'). The お~ prefix is fossilized into the word — you don't hear plain しゃべり as a noun in this sense. まだ + ~ている here pictures the chat as still in progress, with a faint shade of 'still going on' or 'still at it' that can color into mild exasperation depending on context.