You're right about "chance" being a noun.
"Other" occasionally is used as a pronoun -- but not very often.
Check these definitions to see how "other" is most commonly used. Does that part of speech fit your sentence?
http://dictionary.reference.com/browse/other
The word "chance" is a noun right? The sentence is "People at a party welcome a chance to make a big impression." And "other" would be a pronoun... right? It says "If you let other people impress you, they will be impressed by your graciousness."
2 answers
Chance can also be used as a verb and an adjective. In this case it IS a noun.
Other in that case would be an adjective.... it describes people.....ie, these people, those people, some people, other people.
Other in that case would be an adjective.... it describes people.....ie, these people, those people, some people, other people.