Thinly slice the onions.

In a heavy saucepan, melt butter over medium-low heat.

Add the sliced onions and cook until golden brown, stirring occasionally.

Add the green beans, fresh rosemary sprig, and chicken broth (or water) to the saucepan.

Cover the saucepan and cook over medium heat until the green beans are tender.

Remove the cover from the saucepan.

Add the chopped black olives to the green beans.

Continue cooking until the liquid has evaporated.

Season with salt and fresh ground black pepper to taste.

Serve hot.