Combine apricots, 2 cups sugar, orange rind, and juice in a large saucepan. Bring to a boil; reduce heat, and simmer 25 minutes or until liquid is absorbed, stirring frequently. Remove from heat, and cool completely.
Drop mixture by teaspoonfuls onto waxed paper, and allow to dry at room temperature 1 hour. Shape mixture into balls, and roll in powdered sugar. Press a pecan half into each ball.
Note: Apricot Balls are best when prepared one day before serving so that they can dry overnight. A food processor may be used to finely chop apricots.