Preheat the oven to 400°F (200°C), line a baking sheet with parchment, and squeeze excess moisture from the grated zucchini.
Whisk flour, baking powder, and salt in a large bowl, then cut in the cold butter until small pea-sized pieces remain.
Add the shredded cheddar, zucchini, and chives, tossing lightly so the ingredients are coated with flour.
Pour in the buttermilk gradually and stir just until a shaggy dough begins to form without becoming smooth.
Turn the dough onto a lightly floured surface, gently pat it into a thick round, and cut it into eight wedges.
Arrange the wedges on the baking sheet, chill them for 10 minutes, then bake for 18–20 minutes until golden.
Cool briefly before serving warm with butter, eggs, soup, or salad.