Preheat and Prep: Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan or line it with parchment paper for easy removal.
Prepare the Zucchini: Shred the zucchini with a grater. Do not squeeze out the moisture, as it keeps the bread tender and moist.
Mix Wet Ingredients: In a large bowl, whisk together the eggs, sour cream, and melted butter until smooth. Stir in the shredded zucchini and diced chives.
Combine Dry Ingredients: In a separate bowl, whisk the flour, baking powder, baking soda, salt, and garlic powder until well combined.
Combine Wet and Dry Ingredients: Gradually add the dry mixture to the wet ingredients, stirring gently until just combined. Fold in the shredded cheddar cheese evenly throughout the batter.
Bake: Pour the batter into the prepared loaf pan and smooth the top with a spatula. Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Cool and Serve: Let the bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely. Slice and enjoy warm or at room temperature.