Here's one of the many recipes that turns up when 'chewy snickerdoodles' is googled.
Recipe courtesy of Recipezaar http://www.recipezaar.com/113751
1 cup shortening
1 1/2 cups sugar
2 2/3 cups flour
2 teaspoons cream of tartar
1 teaspoon baking soda
1/4 teaspoon salt
1 tablespoon sugar (to roll cookies in)
1 teaspoon cinnamon (to roll cookies in)
Preheat oven to 400.
Mix shortening, sugar, and eggs.
Sift dry ingredients, stir into first mixture.
Roll into balls the size of walnuts, and roll in mixture of 1 Tbl sugar and 1 tsp cinnamon.
Bake 2" apart on an ungreased cookie sheet 8-10 minutes.