Take an unnecessary chance could work as good English, but it depends on the context.
I can imagine two people mulling over a course of action with a risk involved. For example, suppose they want to install a new ceiling fan in their house, but neither one of them has much experience in electrical work. They are debating whether this should be a do-it-yourself job, or if they should hire a qualified electrician. One of them might say:
I think we could probably do this ourselves, but I don't want to take an unnecessary chance.
Here, the risk has an enormous downside – their whole house could burn down! Even if that outcome is improbable, they would rather hire someone who knows what they are doing, just to be safe. The "chance" is unnecessary, because there are plenty of qualified electricians in their city.
On the other hand, I don't think this wording works nearly as well when the negative consequences of the risk are rather trivial. In other words, if my son told me:
I was thinking about asking Debbie to the prom, but I don't want to take an unnecessary chance.
that sounds like he is overdramatizing his fears of rejection. It would make more sense for him to say something more along the lines of:
I was thinking about asking Debbie to the prom, but I'm afraid she might say no.