What an aside and the chorus have un comon is that they both address the audience.
An aside is a dramatic device in which a character speaks to the audience. By convention the audience is to realize that the other characters on stage cannot hear the character´s speech. An aside is usually a brief comment, rather than a speech, such as a monologue or soliloquy.
The chorus, in drama and music, is made up of those who perform vocally in a group as opposed to those who perform singly.