The A does stop in Chinatown.All you need to do is take the A and get off at Canal St. Canal St. goes through all of Chinatown.The A stop at Canal St is right near 6th Avenue, so you will be at the western side of Chinatown.However, if you want to get to the other side of Chinatown, you can transfer to the B or D and get off at Grand St.You can also transfer to the N/Q/R/W/4/5 and get off at Canal St, and those trains run through the east part of Chinatown.
Where the A train crosses Canal Street I wouldn t really call Chinatown anymore. The area has spread, but at best you are on the fringe. If you are coming from Brooklyn, I would recommend that you change at Broadway Nassau for the uptown #4 or #5 and take that to Canal Street. From points north there are a couple of things that you could do. Change at 14th street for the Brooklyn bound L train. Take that to Union Square and take the downtown #4 or #5 to Canal Street. Another thing you could do is to switch trains at Fulton Street, Broadway Nassau as before and take the Uptown #4 or #5.
Take the A train directly to Canal Street, which is the western end of Chinatown.I hope this information is very helpful.Good luck