I want to know if there is an expression I can use that is similar to "there is no chance in hell". How would a native French speaker convey this idea?
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.
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
la semaine des quatre jeudis
To stick with a hell-related expression, you could also use
Il neigera en Enfer avant que...
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
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!”)
Tu peux rêver ! (In your dreams!)