Preheat the oven to 375 degrees F.
Combine the flour, baking soda and salt in a small bowl. Beat the butter, brown sugar, granulated sugar and vanilla extract in a large mixer bowl until creamy. Add the eggs. Gradually beat in the flour mixture. Add the oatmeal, cherries and chocolate chips to your desired consistency and liking, and mix. Drop by a rounded tablespoon onto ungreased baking sheets.
Bake until golden brown, 18 to 20 minutes. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely.
An alternative for the oatmeal is to put approximately 1 1/2 cups of oatmeal in a blender and 'chop' so that the oats are more fine, but do not blend until powdery, then add to mixture.