Preheat the oven to 375.
Cut the baguette crosswise into 12 slices about 1/4 inch thick. Place on a baking sheet and brush with olive oil. Season with salt and pepper and toast in the oven until golden, about nine minutes.
Heat two tablespoons oil in a medium skillet over medium heat and add the shallot. Cook until soft, stirring constantly. Add the mushrooms and continue to cook, stirring occasionally, until tender. Season with salt and pepper.
Place a round of goat cheese on top of each crostini. Top with a tablespoon of the mushrooms. Sprinkle with the chives.