Given an if-then statement "if p , then q", the CONVERSE statement is "if q, then p".



In your case, the converse statement to the given one is 

      If Mary lives in Chicago, then she lives in Illinois.



So, you correctly made the required transformation.



Note, that although the given statement is correct (is TRUE), the converse statement in your case is NOT TRUE, i.e. is FALSE.



It is not always the converse statement to the given statement is true, even if the direct (the original) statement is true.

It is exactly the case with your original and converse statement.



When the direct and the converse statements are both TRUE, they called EQUIVALENT statements.



For example, this direct statement

    If a triangle is isosceles, it has congruent base angles


is EQUIVALENT to its converse statement

     If a triangle has congruent base angles, it is isosceles.



Not every direct statement is equivalent to its converse statement (!)