Answer:
Prepositional phrase: to Chicago.
Preposition: to
The object it governs: Chicago
Step-by-step explanation:
The prepositional phrase "to Chicago" serves the grammatical purpose of indicating the place where the action suggested by the verb takes the place. So the action is "traveling" and the prepositional phrase indicates where this is happening - "to Chicago". "Chicago" is a noun indicating name of the place and the preposition "to" sits before the noun, so that it can help to indicate the place.