The abaya "cloak" (colloquially and more commonly, Arabic: عباية ʿabāyah , especially in Literary Arabic: عباءة ʿabāʾah ; plural عبايات ʿabāyāt , عباءات ʿabāʾāt ), sometimes also called an aba, is a simple, loose over-garment, essentially a robe-like dress, worn by some women in parts of the Muslim world including in North Africa and the Arabian Peninsula. Traditional abayat are black and may be either a large square of fabric draped from the shoulders or head or a long kaftan.
Any dress which fulfills the conditions of Hijab is allowed as far as it covers the whole body except the face and the hands and it is not tight and not transparent.
I have a long pdf document on this which I can send you. Please write to firstname.lastname@example.org
A woman in presence of non-mahram must cover all her body except face and hands(wrists down) -even feet- with loose clothes so that the body shape shall not be seen underneath the clothes.
So Abayah or Chador is not mandatory.