Updated

We've seen houses that sit alongside rolling rivers, but this stone cottage in Fairfield, CT, sits right on top of one. For $2 million, you can sip morning coffee in your kitchen and watch the water flow underneath.

It's a home that's impossible to reproduce. "With all the regulations, not only would you not be able to build a house over a brook, you'd have to set it back significantly," listing agent Andrew Whiteley of William Raveis Real Estate says. Because the building was converted to a residence a while back -- Whiteley guesses during the 1940s -- it's been allowed to stay as is.

Built in 1836, the 3,000-square-foot home was a mill producing plaster made from horsehair and oysters, presumably for the surrounding population in the (now historic) district of Greenfield Hill. The mill's turbine has been removed, and the bridge has been transformed into a kitchen.

A bay window provides a spectacular view of the water as it tumbles from the property's pond into the river below.

The kitchen has french doors leading to a stone patio. There you can listen to the sound of water falling over the rocks as it journeys to Long Island Sound. Bird calls and the rustling of wildlife in the nearby woods provide an accompaniment to the sound of the water.

The kitchen connects to the master bedroom addition, which overlooks the water and where the sound of rushing water will lull you to sleep.

While having a river underneath your home might raise a red flag, Whiteley say this one hasn't posed a threat yet. Because it's man-made, the water follows a "clearly defined" path, which keeps it from flooding, he says. When Hurricane Sandy devastated the Northeast in 2012, the house had no issues, Whiteley adds.

In the two-bedroom main house, cherry wood doors imported from a French cathedral open to the living area, which features a vaulted ceiling with redwood beams, French walnut floors, and a charming fireplace.

Also on the property are a converted barn and detached two-bedroom guest cottage. The barn has been converted into a two-car garage with a loft for storage. Whiteley says the barn was constructed around the turn of the century, while the guesthouse was likely built during the 1940s.

At some point, a blacksmith operated on the almost 2-acre property. "People are still finding horseshoes when they're gardening in the area," Whiteley says.

The home, which was featured in Architectural Digest in 1990, has been on and off the market since 2013. Whiteley says the sellers, who bought the home in 2000 for $2.3 million, are looking to retire.

"It's incredibly unique, [but] it's difficult [to sell], because you have to find that right kind of special buyer," says Whiteley.