Cut a 1-inch thick slice from the top of round bread loaf; hollow out the loaf to use as a bread bowl. Slice the cut-off top of the loaf into cubes for dipping.
Combine cream cheese, Cheddar cheese, ham, green onion, and chives in a microwave-safe bowl.
Heat in microwave on high power for about 15 seconds to warm ingredients for easier stirring.
Spoon cheese mixture into prepared bread bowl; place on a baking sheet.
Bake filled bread bowl in the preheated oven, stirring occasionally, until bread bowl is toasted and dip is bubbling, about 30 minutes.