Place bread cubes in the bowl of a food processor fitted with the blade attachment. Process until the bread is in crumbs. Pour the breadcrumbs into a large mixing bowl and toss with the beaten egg until evenly moistened.
Wipe out the food processor bowl then add the garlic, anchovy fillets, olives, capers, salt, red pepper flakes, and the leaves from the sprig of oregano. Pulse until the mixture is finely chopped but not a paste. Add to the bowl with the bread mixture.
Add the ground chicken and gently mix with your hands until everything is well incorporated.
Roll one small tester meatball. Heat the 2 tablespoons of oil in a large (3-4 quart) shallow braising pot or Dutch oven over medium heat. Cook tester meatball until it is browned on all sides and cooked through. Taste the meatball. Is it perfect? The meatballs will taste salty but when combined with the sauce and the pasta will be just right. If you'd like them spicier, add more red pepper flakes.
Gather mixture into round balls, about 3 inches in diameter, and place on a baking sheet. I like to make 8 large meatballs (2 per person). Make smaller or larger meatballs if you prefer.
Return the pot that you cooked the tester meatball in to medium heat and add meatballs in batches if necessary, being careful not to crowd. Cook meatballs turning frequently until browned on all sides. You don't need to cook them all the way through at this point they will finish cooking in the sauce, just make sure they are nice and browned. Remove the meatballs to a clean bowl as they finish cooking and continue with the next batch until all meatballs are browned. Set aside while you make the sauce.