Those Mexican ladies with the coolers, carts and unmbrellas? They are selling hot, hand-made tamales. Lots has been said about where to find the best. North Clark in Uptown, corner of Ashland and Division, many places on Lawrence and inumerable places on the South Side in Pilsen, La Villita, Bridgeport, East Side, etc., etc.
The greatest variety of high quality hand made tamales is probably offered by the vans that hang out by Max Gerber (Milwaukee near California) on weekends. Good luck. Mornings are your best bet, as tamales and champurrado are breakfast. As the ladies make them with fresh, delicate masa the night before, you get them hot from the water. They freeze well if you want to keep them for later.
Or you can get inferior ones, cold, at Fox & Obel for big money. I really like F&O (though they stopped carrying Anson Mills (and all other) grits), but I can't fathom buying tamales there.