Final answer:
The words correctly capitalized in the sentence are Chandler, State, and Arizona. When used in the full term 'State of Arizona,' the word 'state' is capitalized as a proper noun, just like Chandler and Arizona.
Step-by-step explanation:
In the sentence "Chandler is not a big city in the State of Arizona." the words that are capitalized correctly are Chandler, State, and Arizona. Therefore, the correct answer is A. Chandler, State, Arizona. The names of cities like Chandler and states like Arizona are always capitalized because they are proper nouns. The word 'state' can be tricky, but when it is part of the full name of the governmental unit, as in 'State of Arizona,' it is considered a proper noun and thus is also capitalized.