Place the bacon in a non-stick pan over medium heat. Cook on both sides until crispy and golden brown. Place on paper towels to drain any excess grease.
Remove the bacon grease from the pan except for about 2 teaspoons. Crack the eggs into the pan and cook until the whites start to set. Add 1 to 2 tablespoons of water and cover with a lid to firm the whites of the egg completely. Season with salt and pepper.
Meanwhile, add the cream and chives to a saucepan over medium heat. Bring to a simmer and reduce the cream to a thickened creamy consistency. Remove from the heat and season with salt and pepper to taste.
Lightly toast the english muffins.
Place the eggs and bacon on the english muffins, lightly spoon the sauce over top, and serve with blackberries.