I'm guessing that in nearly all circumstances 'take' means 'take'.
Even in 'take a chance on me' 'take' doesn't mean 'give'.
'Take a chance on me' is not the same as 'give me a chance'.
Take a chance on me suggests putting oneself (or ones money) at risk in allowing 'me' an opportunity.
'Give me a chance' does not really mean that the person giving the chance is risking anything of their own.

My understanding only.

Cheers
Nigel