In a large skillet, over medium-high heat, stir the anchovies into the olive oil, cooking until anchovies melt into a paste.
Add garlic and hot red-pepper flakes; cook until garlic is softened, about 1 minute.
Add tomatoes. Bring to a boil. Reduce heat and simmer, uncovered, until slightly thickened, about 7 minutes.
Stir in the capers and olives. Cook for about 1 minute longer. Serve over spaghetti, garnished with chives.
Additional Tips
A Pouilly-Fumé pairs well with this briny dish.