Seven miles off the shore of Cape Cod in Massachusetts, Martha’s Vineyard is a roughly triangular-shaped, 96-square-mile Atlantic Ocean island with six towns. One of these communities is Chilmark, whose 02535 ZIP Code has the priciest residential real estate in all of New England, according to Realtor.com. (News Corp, owner of The Wall Street Journal, also operates Realtor.com under license from the National Association of Realtors.) Rural and private, Chilmark has a pastoral landscape: rolling hills, stone walls and sheep grazing on hillsides. It also encompasses the small working fishing village of Menemsha, which has a public beach where people congregate to watch spectacular sunsets across the Vineyard Sound.

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