Make the sauce: Whisk the heavy cream and sour cream in a large skillet and season with salt and pepper. Simmer over medium heat, whisking, until the mixture thickens and all the sour cream melts, 2 to 3 minutes. Add a few grates of lemon zest and some of the lemon juice. Taste for seasoning. At this point the sauce should be thick enough to coat the pasta.
Meanwhile, cook the pasta: Bring a large pot of water to a boil. Add 2 tablespoons salt and bring the water back up to a boil. Add the pasta to the pot and cook until al dente, stirring occasionally to make sure it doesn?t clump or stick to the bottom, about 2 minutes. Drain the pasta in a colander, reserving 1/2 cup of the cooking water.
Add the pasta to the skillet and toss to coat with the cream sauce. Shut off the heat and allow the pasta to rest in the sauce for 2 minutes, tossing to coat from time to time. If the sauce is too thin, simmer over low heat for 2 additional minutes. If it is too thick, simply thin it out with some of the reserved pasta water. Taste for seasoning. Add more salt or lemon juice, if needed.
Spoon a small amount of caviar onto 4 serving plates. Use a fork to twirl the pasta and make a large forkful. Use your index finger to gently coax the pasta off the fork and on top of the caviar on the plate. Repeat with the remaining plates. Spoon any leftover sauce over the pasta. Note: The sauce thickens quickly, so keep it loose with a little pasta water, if needed, as you plate. Sprinkle with the chives and a touch more grated lemon zest.
This recipe is meant as a first course or appetizer for a bigger holiday meal; if you want to serve it as a main course, consider doubling the recipe.