Opening for Gary Allen.
This was the band's first show ever, at the time called Tony Flow and the Miraculously Majestic Masters of Mayhem. It was supposed to be a one-time opening act. The date listed on the official website is February 13th but the timeline on "An Oral Visual History" book says February 6th.
Both dates were on a Sunday and the "Rhythm Lounge" only opened on Thursdays. Blackie Dammet also briefly mentions this on his autobiography: "that memorable Thursday night in February 1983 when the dynamics of music changed dramatically and altered the balance of the L.A. scene", which makes us pretty sure that neither of those are correct.
The only option between those two dates would be the 10th, but What Is This? played a gig in L.A. that day, so it would be unlikely that both shows happened on the same day. Our best guess is it happened on the 3rd, but the real date still remains unconfirmed.