No. I wouldn't. I don't do well with ultimatums.
However, if they are asking you for a legitimate reason rather than because they can't deal with their own insecurities, it's up for discussion. If it's because they're insecure, the reason for their insecurities can be discussed to see how you two as a couple can move forward from them.
A legitimate reason would be something such as if you had lied about your relationship with that friend or lied about anything you've done with them. In that case I can see where the trust issue came from in the first place, and it definitely needs to be dealt with - but then you have a
much bigger problem than your SO asking you not to talk to your friends.
Having been in that situation before, I can say that it's not fun and destroys the trust in the relationship almost completely. I still don't think it's a fair or reasonable request, but I think we all ask for unreasonable things once in a while in relationships.
If it really was an issue, I'd find some sort of middle ground. Like only talking to that person on my phone, so my OH can check it since he snoops on my phone all the time. Or just in person with the OH there. Really if that doesn't work there are some issues in the relationship.
I'd have a problem with the snooping on the phone more than "don't hang out with so and so."
One of my friends doesn't want me to text him because his wife might see the texts, and I flat out told him that there's nothing for her to be jealous of because I don't feel that way about him and I'd be happy to let her know that if she'd ever like to call me and ask me why I'm texting her husband. About totally mundane things, like cars. And vodka. Unless those things are now code for adultery.