When you refer to your most famous TV show in your stand-up title, surely it’s perfectly legitimate to be asked questions about it? Fortunately, Mary Lynn Rajskub is free, easy and very forthcoming with her opinions and memories about 24, the conspiracy thriller which ran for nine full seasons (24 nerds will claim it’s eight and a half given that the most recent London-set plot lasted only 12 episodes). The innovative show (each episode spanned a real-time hour, minus ad breaks and, presumably, toilet breaks for agents in the field) introduced millions to Chloe O’Brian, the most sarcastic counter-terrorist officer and computer whizz the fictional world has ever known.

All of which made life a little awkward when Rajskub’s fledgling stand-up career ran parallel to being Chloe. ‘If audiences are really into 24, I’ve developed a way to satisfy their sweet tooth,’ she insists. ‘When I first started stand-up, there was a disconnect and they’d be like, “why is Chloe on stage?”, so I’d address it and indulge them for 20 minutes. But those times could also be the most fun because I’d then take people off down a different road with my material.’

Mary Lynn / Chloe was invaluable to both the series and its permanently scowling figurehead Jack Bauer (played with a renegade menace by Kiefer Sutherland) as she quickly turned around initial audience antipathy to become a 24 mainstay. Appearing in a total of 125 episodes, she was second only to Bauer as the longest-running character in a show that was not afraid to dispatch major personnel, long before Joffrey had Ned Stark’s head on a spike. The sad news for 24 fans is that any future movie or series will have to do without Chloe. Rajskub’s description of this scenario is shrouded in a 24-esque fog of confusion.

‘Will Chloe be back? I would go and ahead and say absolutely not and that’s part of the reason why I’m doing the festival as I’m trying to carve a new path for myself. Sadly it’s not my choice to have Chloe continue or not, that’s down to the people in charge, and they really did not have an interest in that. 24 fans would want it to happen and, actually, I was surprised how not tired I was of playing her and could see her further development if she was in charge.’

So, the producers have categorically said ‘no more Chloe’? ‘They haven’t come out and said that they won’t write more Chloe storylines, but it’s been made clear to me without them actually saying anything. The job is over and I move on; I don’t sit here and expect to get a call as it’s not a conversation I expect to have with them … ’ Perhaps only Jack Bauer and his interrogation ‘methods’ would be able to get to the true heart of that one.

Despite being central to the most humourless show in TV history (prior to Chloe injecting sarcasm into proceedings, we only really had Bauer’s CTU nemesis George Mason playing the witty card), Rajskub’s background is firmly rooted in comedy. Her CV is packed with appearances in the likes of Dude, Where’s My Car?, Modern Family, Flight of the Conchords, The Larry Sanders Show and Brooklyn Nine-Nine, though there is the odd dramatic intervention such as Helter Skelter, where she played a member of the murderous Manson Family, and the Harrison Ford-helmed crime thriller Firewall.

She admits that 24 Hours with Mary Lynn Rajskub will only mention her time on the show in brief passing (‘I’m not going to be playing the DVDs and then taking questions about it’) as she intends her Fringe stand-up debut to focus on her own life away from screen endeavours.

‘It’s a very personal story based on relationships and how they kind of suck, so I’m writing from that perspective I’m reconciling all the crazy things I’ve done in my past with the fact that I’m probably in the only mature relationship I’ve ever had. I did a one-woman show which dealt with accidentally getting pregnant to my husband who I’d only known then for about three months, so this show is the next stage of my life. It’s really about the mechanics of relationships and how we can love somebody after once hating them and how we can get longevity and not just crash and burn.’

Crashing and burning is something that many comics try desperately to avoid when playing a long, gruelling month at the Fringe. Have a look at Hannibal Buress Takes Edinburgh on Netflix for proof of someone really not coping with the August slog. ‘It’s going to be a completely new and unique experience for me,’ Rajskub admits. ‘I’ve done a lot of comedy clubs where I’ll do six shows at weekends but nothing will be like this. I’ll drink lots of liquids and maybe take a Pilates class. Other than that, I’m just going to pretend I’m on Broadway.’

24 Hours with Mary Lynn Rajskub, Assembly George Square Studios, George Square, 0131 623 3030, 6–28 Aug (not 15), 8.20pm, £11–£12 (£9–£10). Previews 3–5 Aug, £8.