彼女はおしゃべりだ。

English Translation

She is talkative.

Is the お necessary?

@ericaw
You cannot omit お, which is not inserted here as a polite prefix, but is converting a verb etc. into a noun (the person who XXX). Example phrases with the same pattern are:

あの人はお人好しだ。(おひとよしだ)= That person is too kind/generous or believes everything.

彼女はおてんばだ。= She is a tomboy.

あのおじさんはお節介焼きだ。(おせっかいやきだ)= That middle-aged guy sticks his nose in everything.

Those are negative characteristics, so you don’t need 尊敬語 (polite prefix). But お人好し、おてんば、and お節介焼き with お are “the person who has a nature of X”.