Green’s Dictionary of Slang

big A n.

[on model of big C n. (2); big H n.]

1. (US) Acquired Immuno-Deficiency Syndrome (AIDS).

[UK]Observer 23 Feb. in Partridge Concise Dict. Sl. (1989).
[US]T. Williams Crackhouse 123: They’re the ones who can turn a person down if they don’t like him or if he don’t look right – if the guy looks sickly or look like he’s got the big A.
[US]W.D. Myers Handbook for Boys 92: ‘If they don’t kill each [...] they’re liable to end up with AIDS. And the big A will definitely take you on out of this world’.
[SA]K. Cage Gayle.

2. see arse n. (9)