Chop rapini into 1 1/2 inch pieces, all the way up to the leaves and florets. Place in a colander and rinse well. Spin dry or transfer to a towel to shake out most of the water. Rapini should be mostly dry before cooking.
In a large sautee pan, with deep sides, heat oil to medium. Add in garlic and chilis, stirring for about 30 seconds. Be careful not to burn the garlic, keep heat at medium.
Add rapini and broth, cover and let steam for 5 minutes. Uncover and continue to cook for 2-3 more minutes, or until half of the liquid has evaporated.
Add vinegar and season with a good pinch of salt and pepper. Stir and remove from heat. Serve hot.