Sweat the leek in 2 teaspoons of butter over low heat in a tightly covered straight-sided saute pan for 6 minutes, stirring once or twice.
Add the rice and raise the heat to medium, stirring often for 3 minutes. Add 1 cup of stock, season lightly with salt and pepper, and stir until all of the liquid has been absorbed.
Add the remaining broth, 1/2 cup at a time, stirring constantly after each addition. When all of the liquid is absorbed, add the zest and continue to cook for about 10 minutes more, until the rice is al dente.
Stir in the lemon juice. Season well with salt and pepper, add the chives, stir in the remaining 2 teaspoons of butter until it melts, and serve hot.