Home made pesto. Whizz up a bunch of parsley or basil or both, some pine nuts, grated parmesan, olive oil, plenty of salt, squeeze of lemon.
Or you can buy this sauce called spicy Ayvar. It's made of aubergines and peppers and chillis and comes in a jar. That's lovely with chicken.
Or a creamy mushroom sauce? Just fry mushrooms with garlic and add a splash of white wine and cook down a bit, then finish with a splash or glug of cream. Sprinkle with parsley.