The scene in Saint-Moritz, in Switzerland’s Engadine Valley, feels as old as time. It’s where Czar Nicholas II dreamed of constructing a summer residence, and Brigitte Bardot skied with Gunter Sachs.

But today, while aristocrats and billionaires fight over $10,000 hotel rooms and luxury stores line the main road, a five-story cement house smack in the center of town stands conspicuously unkempt.