Heat the olive oil in a 9-inch skillet over medium heat. Add the diced green chilies and sauté, stirring for a minute. Drain half the liquid out of the can of beans and add the beans and the rest of the liquid to the skillet. Stir to combine.

With the back of a spoon, make 4 indentations in the beans and crack the eggs into the indentations. Season to taste with salt and pepper. Cook until the egg whites are set and the yolks are still runny, about 10 minutes.

Peel, seed, and slice the avocado. Place the avocado slices on top of the beans, scatter the cilantro on top, and serve.