Put the cut potatoes into a large pot, cover them with cold water, and add a large pinch of salt. Bring to a boil and simmer until the potatoes are fork tender, about 20 to 30 minutes. Drain well. Meanwhile, in a small pot heat the cream, butter, garlic, and thyme. While the potatoes are still warm, press them through a potato ricer or food mill into a bowl. Stir in the warm cream a bit at a time, straining out the solids, until the potatoes are fluffy. Season with salt and pepper and gently fold in the chives. Serve immediately.