Heat stock in a medium saucepan, and keep warm over low heat.
Heat 4 tablespoons of butter in a medium straight-sided saute pan over low heat. Add leeks, and cook, covered, until translucent, about 6 minutes. Add rice, and raise heat to medium-high, stirring often for 3 minutes.
Add about 1/2 cup hot stock, or just barely enough to cover rice. Cook, stirring, until stock has almost completely absorbed. Add lemon zest, stirring to combine. Continue cooking and stirring rice in this manner, adding 1/2 cup stock at a time, for 15 to 20 minutes. At this point the rice should be tender but still a bit firm to the bite. Stir in lemon juice. Season well with salt and pepper. Add chives, and stir in the remaining 2 tablespoons butter until it melts. Serve hot, sprinkled with Parmesan and lemon zest.