I’m not aware of any French idiom with the same meaning that refers to hell. The typical idioms for “things that have no chance of happening” are:

quand les poules auront des dents

and

la semaine des quatre jeudis

I would suggest you for this kind of discussion:

Q: Will you go out with me?

A: There is no chance in hell!

the following in French:

Q: Veux-tu sortir avec moi ?

A: Même pas en rêve !

Or, in a more formal discussion:

There is no chance in hell that government approve this proposition.

Il n’y a pas la moindre chance que le gouvernement approuve cette proposition.

To stick with a hell-related expression, you could also use

Il neigera en Enfer avant que…

litterally meaning

It’ll snow in Hell before…

The positive expression “une chance d’enfer” is the only one that I know that involves “chance” and “hell”… but that’s more like “a hellish luck”.

More seriously, to express that “there is no chance in hell” I might say

Il n’y a pas l’ombre d’une chance

Tu peux rêver ! (In your dreams!)

I’d say that in place of “there is no chance in hell”, in similar situations, we would often suggest someone “not to even think about it”. (Note that it doesn’t necessarily convey the same “I will not allow it” meaning as in English.)

— Tu devrais lui demander.
— Parler à ce gars-là. Bah, n’y pense même pas !

(“There is no chance in hell I will talk to him!”)

Sometimes the suggestion goes to a third person:

— Il dit pouvoir remporter la médaille d’or l’an prochain.
— Ah ah ha ! Qu’il n’y pense même pas !

(“No chance in hell this could happen!”)