Combine milk, sugar and rice in a heavy saucepan. Bring to a gentle boil over medium heat. Reduce heat to simmer and cook uncovered for 1 hour, stirring occasionally. (The milk should just barely simmer, with bubbles breaking only at the outside edge of the surface. After an hour, the rice should be soft.)

Add raisins, increase heat to medium heat, and cook, stirring frequently until rice has absorbed most of the rest of the milk, but not all, and the pudding is creamy (about 30 minutes longer).

Remove from heat and stir in vanilla extract. When cool, pudding will thicken, but will still be very creamy. Serve warm or well chilled.