Montreal airport (YUL) to chinatown?

Taxi is indeed expensive. But don't rent a car! Not unless you need to drive off the island of Montreal. If you are headed to Laval, the Eastern Townships, or the Laurentians, then you need a car. But the city of Montreal has a great public transit system and a car will just cost you $50+ per day for a rental, more if you get the insurance, and the hotel will likely charge you $10+ for parking fees per day.

Expect to pay a fixed rate of $40 for a taxi to get from the airport all the way to downtown area. Chinatown is right in the downtown area. You could just let the meter run, but odds are you won't get a better rate than about $38 for that route, and likely would be closer to $50.
http://www.admtl.com/Passengers/AccessAndParking/TaxisAndLimousines.aspx

I would say take a taxi if you are a couple of travellers or have a lot of luggage to deal with. If you have only a bag or two and can carry everything yourself, then you can save some money by taking the city bus that travels from the airport to downtown. They call it Bus # 747. For $10, they will get you from the airport all the way to the bus depot on the far side of the downtown area. It stops at various hotels too. The Chinatown area is between stops # 7 and #8, just south of the bus route.
http://www.stm.info/sites/default/files/planibus/en/747.pdf

If you plan to go to the museums while here, there is a pass that includes public transit. It should be available at the airport. But you can also buy it in advance online.
http://www.museesmontreal.org/en/The_Montreal_Museums_Pass__your_cultural_passport_for_easy_access_to_38_museums.htm

Do you know what hotel you are staying at? If so, you may want to contact them and ask them if they have a shuttle service from the airport. That might be free or just cost you whatever you tip for the driver.

Taxis arent always the most expensive. I use taxis alot whenever i go travelling and in montreal especially. One of my favorite apps for taxis is OnCabs. I would check them out and see if it would work for you.

Chinatown Car Service