Bring a large pot of water to a boil. Add a couple generous pinches of salt.
Using a peeler, peel off thin strips of skin from the lemon. Apply gentle pressure, trying your best to get mostly the yellow skin, and less of the white pith underneath, which has a more bitter flavor. Put 1/4 cup olive oil in a small saucepan over medium heat. Warm for about 1 minute. Put the lemon peel strips into the warm oil, it should bubble gently when you add them. If not, wait a minute for the oil to get warmer. Take the pan off the heat and set aside once the lemon peel is added. Once the oil cools, strain it and set aside.
Peel and smash garlic clove. Cut cherry tomatoes in half. Roughly chop capers; pit and roughly chop olives.
Heat a 10-inch skillet over medium-high heat. When pan is hot add 2 teaspoons olive oil, followed by garlic clove and red pepper flakes. Swirl pan or stir for 30 seconds to avoid burning garlic. Add tomatoes, capers, and olives. Reduce heat and simmer for 8-10 minutes.
Meanwhile, cook pasta in boiling salted water until tender, or according to package instructions. Drain pasta and put in large serving bowl. Toss with warm tomato sauce and drizzle with 1-2 Tablespoons of lemon oil (reserve rest of lemon oil for a salad dressing). Season with salt and pepper. Mince chives for garnish and serve immediately.