Peel and cut the potatoes and parsnips into even sized pieces. Put them into a large pot, cover them with cold water, and add a large pinch of salt. Bring to a boil and simmer until the vegetables are fork tender, about 20 to 30 minutes. Meanwhile, in a small pot gently heat the cream and butter over low heat. When the vegetables are done drain them well. Put the vegetables back into the pot over medium heat. Gently stir them to remove any excess moisture; be careful not to burn them. While the potatoes and parsnips are still warm, press them through a potato ricer or food mill into a bowl. Add the warm cream a little at a time and beat with a wooden spoon until the potatoes are fluffy. Season with salt and pepper and gently stir in the chives. Serve immediately.