Preheat oven to 375°.
Coat a 6-oz. ramekin with butter. Pour whipping cream into ramekin.
Crack eggs into ramekin, coaxing yolks toward the center, using a spoon if necessary.
Sprinkle eggs with salt and pepper, top with chives, then cheese.
Bake until set around edges and still a bit jiggly in the center, about 12 minutes. (For firm yolks, bake an additional 3 minutes.) Let sit 2 to 3 minutes to set and serve immediately.
For easier oven transfer, set dish, or dishes if making more than one serving, on a large baking pan.
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