A small factor is rounding error. There is probably not exactly 60 g of protein any more than there is exactly 9 calories per gram of every single type of fat.
Another may be over-estimation. The could just be rounding up to 300 to provide a nice number or cover themselves, since some chicken breasts may be larger or fattier than others.
Finally is how calories are measured. They put the chicken breast in a calorimeter and burn it, and see how much heat it generates. This is not a perfect process and, also, some things that burn aren't used as energy by your body. (One example would be fiber, although there's none of that in chicken). So the number of calories is just an estimate of how many calories are provided to your body, and the estimate is not actually based on some sort of human study or model. Some food companies might skip the calorimeter and just add up the numbers like you did, though.