Preheat the oven to 400 degrees and line 2 large baking sheets with parchment paper. In a bowl, combine the goat cheese, chorizo and chives; season with salt and pepper.

Lay a sheet of phyllo on a clean, dry work surface and brush it with melted butter. Top with 2 more phyllo sheets, lightly buttering each sheet as you go. Cut the phyllo into 6 rectangles. Place a tablespoon of the goat cheese filling at the base of each rectangle and roll up the phyllo, folding in the sides. Set the rolls on the prepared baking sheets. Repeat twice more to make 18 rolls total. Brush the rolls with butter; bake for 10 minutes, until golden. Serve hot.