Melt the butter in a small Dutch oven over medium heat. Add the onion and cook, stirring occasionally, until softened, about 12 minutes. Increase the heat to medium high, add the mushrooms, 1/4 teaspoon salt and a few grinds of pepper and cook, stirring often, until the mushrooms release their liquid but do not brown, about 8 minutes. Add the chicken broth and bring to a simmer. Simmer, partially covered, for 30 minutes.
Transfer to a blender and puree until smooth (be careful when blending hot liquids). Add the Marsala if using and season with salt and pepper.
Pour the soup into 4 bowls. Dollop with the creme fraiche and sprinkle with the chives. Drizzle a tiny bit of olive oil over top.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.