'Chill' is usually a verb or a noun, while 'chilly' is the adjective. A wind which is cold can be described as a chilly wind. The expression 'a chill wind' is an idiom. It's usually found in sentences such as this: "World economies are facing the chill wind of the recession." As with many idioms, the use of grammar and vocabulary is often archaic and therefore non-standard. Think of it as an exception to the rule.

Chill is a verb, a noun and an adjective (cold, cool. Also it's been used as a slang, meaning "to relax" or "to hang out"). Chilly is often utilized as an adjective (expressing quite calm) and an adverb. Then you can use them in an appropriate form.