Use a box grater or food processor to shred the zucchini and carrots.
Place the shredded zucchini in a clean dish towel or stacked paper towels. Wrap towel around the zucchini, and using your hands, squeeze out as much liquid as possible.
Transfer the zucchini to a large bowl, with the carrots, garlic, flour, eggs, chives, salt & pepper. Mix until combined.
Line a plate with paper towels. Place a large sauté pan over medium-high heat and add the olive oil. Once the oil is shimmering, scoop mounds (about 3 tbsp each) of the vegetable mixture into the pan, flattening the mounds slightly and spacing them at least 1 inch apart.
Cook the fritters for 2 to 3 minutes before gently flipping. Continue frying an additional 1 to 2 minutes until golden brown and crispy. Transfer the fritters to the paper towel-lined plate, season lightly with salt and repeat the cooking process with the remaining mixture.
Serve immediately while hot, topping with a dollop of sour cream mixed with more chives.