Chimney on 100 year old home has pulled away from outside wall
You need to find if the chimney is leaning or if the house is leaning.  Use a plumb bob to check - the eye can be deceiving in these situations.   The plumb bob will tell you what you should do.

In the meantime, if you wish, you could put a board or metal flashing on the gap to shed the water while you figure out what to do.

BTW... it's unlikely you could "push" the chimney towards the house as it just has too much mass.