The phrase "given a (the) chance"
I've recently come across the phrase "given the chance" ("Many people are capable of learning a foreign language given the chance") I'm trying to define it as a particular syntactical form, but I haven't succeeded in that. I know that "given" is a past participle, and I understand the meaning of the phrase, but is there a name for this structure? Does it work with some other verbs as well? Could you give me examples with "given a chance" VS "given THE chance" - as a Russian speaker, I still struggle with the articles in English...
Thanks in advance!