Grate the courgette, and spread it out on a few layers of kitchen paper. Lay a few more layers on top, and press down to squeeze out any excess moisture.
Transfer the grated courgette to a large bowl. Add the flour, and mix to coat. Next add the eggs, chopped chives, and a generous amount of salt and pepper, and mix thoroughly.
Drizzle a small amount of oil into the waffle maker, and add the fritter mixture, spreading it around into your desired shape. Drizzle a little more oil on top, and close the lid of the waffle maker. Cook until the waffles are browned on the outside, and fairly firm (they will take a good few minutes, maybe up to 10 minutes depending on your waffle maker).
Serve with a dollop of sour cream or Greek yogurt, if desired.