Preheat the oven to 375 degrees.
In a food processor fitted with a steel blade, blend the oregano and pistachios together until fine and crumbly.
Lightly grease a baking sheet with olive oil. Pat the lamb chops dry, then season with salt and pepper. Place the lamb chops on the oiled baking sheet. Using a butter knife, spread a layer of goat cheese over the top of each chop. Spread the cheese so it is smooth and evenly covers the chops. Press the pistachio mixture into the cheese, forming a crust. Drizzle about ½ teaspoon of the olive oil over the top of each chop.
Place the lamb chops in the preheated oven. Bake for 8-9 minutes for medium rare or 1-2 minutes longer for more well done. Transfer 2 pistachio and goat cheese crusted lamb chops to dinner plates. Drizzle with balsamic syrup and serve warm.