In a large frying pan, cook the chorizo over low heat, crumbling with a fork, until it begins to brown, about 10 minutes. Reduce the heat to a simmer and cover.
Preheat the oven to 375 degrees.
Lay out the sliced baguette on a baking sheet. Brush the tops with olive oil and season with the salt and pepper. Cook until golden brown, about 4 minutes on each side. Remove the crostini from the oven. Spread the goat cheese on each slice. Sprinkle crumbled chorizo on top. Enjoy!