A House is not a machine to live in," wrote the pioneering modernist Eileen Gray in response to Le Corbusier's oft-quoted line about a house being a machine á habiter. "It is the shell of man—his extension, his release, his spiritual emanation." ... Anglo-Irish Gray worked on E.1027's design and construction from 1926 to 1929 with her lover at the time, the Romanian-born architect and magazine editor Jean Badovici, and everything about it was premised on her love of the sea and sun, like its floor-to-ceiling windows and sunken solarium lined with iridescent tiles.  An ingenious skylight staircase rose from the center of the house like a spiraling nautilus made from glass and metal. Instead of a sentimental seaside name, Gray chose a streamlined numerological symbol for her relationship with Badovici: "E" was for "Eileen," the "10" and "2" represented Badovici's initials—according to their place in the alphabet—and the "7" was for "G," so that Gray was, in a sense, embracing him: E.1027.

Despite its auspicious beginnings, the house—one of the most important examples of domestic architecture in the 20th century—is shrouded in the kind of intrigue that one usually associates with Italian castles or crumbling English manors, not sparkling flat-roofed structures in the south of France. Maybe it's the coastal railway cutting too close to the property line, or Gray's own disaffection with Badovici. Maybe it's the German soldiers who used the walls for target practice during World War II; or Peter Kägi, a gynecologist and morphine addict, who bought the house in 1974 and was murdered there in 1996; or the homeless droguers, who squatted there after the house was abandoned and spray-painted the walls with cultish graffiti.

The worst slight of all happened after Gray broke up with Badovici and moved out of the house they designed together. Badovici was in awe of Le Corbusier and invited him to stay on several occasions, and E.1027 became something of an obsession for the architect. Even though he had once praised Gray for the subtlety of her design, Le Corbusier ended up painting eight large wall murals between 1938 and 1939, both inside and outside E.1027, all drawn in shallow depth with Cubist elements, some with charged sexual imagery.

Her supporters feel that the defacing murals should be removed and the house restored to its 1929 condition. But Le Corbusier is more famous than Gray, and the murals have been deemed works of art—national treasures, even—and accordingly preserved and restored. One suggestion was to create scrims that could be pulled over the murals when Gray scholars were visiting and then pulled back again when Le Corbusier scholars were on site. But nothing has been done to resolve the conflict. The house remains shut to the public, mired in disrepair and bureaucratic deadlock.

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Yet in keeping with E.1027's twisted history, the promised rescue was compromised. The restoration has been dragging on for more than a decade. "This is a real scandal, but no one dares talk about it," says Renaud Barrés, a French architect who supervised early restoration efforts and refers to the current program as a "massacre." ... The battle for E.1027 seems intractably bound up with the fight for Gray's legacy—both of which have been colored, and perhaps overshadowed, by Le Corbusier. In the end, she outlived him by 11 years. Le Corbusier drowned while swimming off the beach at Roquebrune-Cap-Martin, just below E.1027, a possible suicide. Gray died peacefully in Paris on October 31, 1976, at the age of 98. On that very last morning she sent her maid out to buy cork and other materials because she wanted to start work on a new project.