Using a small food processor, pulse the black olives. Add two to four tablespoons of olive oil, and continue to process the olives until they turn into a smooth, yet still thick tapenade. Pour the black olive tapenade into a small bowl.
Add the green olives to the food processor and pulse them as well. Then, add two to four tablespoons of olive oil, and continue to process until smooth but thick. Pour the green olive tapenade into a second bowl.
Repeat the same process with the Kalamata olives.
Peel the carrots, and slice them at a steep angle to yield 1/2-inch slices. Top each carrot slice with its own spoonful of tapenade, and garnish the carrot with chopped chives. Keep refrigerated until time to serve. The tapenade can be made up to two days in advance.