方 refers to a person in a polite way and たち makes it plural.
チリの人 a person from Chile
チリの方 a person from Chile (polite)
チリの人たち people from Chile
チリの方たち people from Chile (polite)
It depends on the circumstances, but my translation for the sentence would be this:
Your companions would like hamburg steaks? I thought so...
I hope this will make sense!