If you want a real good, deeper flavour then it pays to plan ahead for a good stock base. When you've had a roast chicken dinner, save and freeze the bones. Then you can use them to make stock i.e. straight from frozen in the water, or bake the bones first till brown for a richer/darker stock. Then proceed in the usual manner.
Incidentally, you can also make up the stock then reduce it down, i.e. boil/simmer until quite thick, gloopy. When cool/cold, can then freeze into an ice cube tray. When solid, empty out and place in a freezer bag, taking out what you need for sauces etc. This then will be a superior stock cube!