What makes a chewy brownie?
One of the most important factors in achieving a fudgy, chewy brownie is cooking time. Essentially you should be slightly undercooking the brownies so they don't dry out in the middle.

Use the cooking times given in recipes as a guide only, because each oven will vary. 5-10 minutes before they 'should' be ready, start testing the centre of the brownies with a toothpick or cake tester: unlike a cake, you want a good amount of sticky crumbs on the skewer (but very little liquid batter). Remember that the cooking process will continue even once the brownies are out of the oven.

Another factor that contributes to chewiness is the sugars you use: adding some sticky, dense, dark sugar will help create a fudgy brownie. The brownie recipe I use, which is pretty damn good, uses 1.5 cups of granulated sugar and .5 cup of packed dark brown sugar.