In a large pot of boiling salted water, cook the orecchiette until just al dente. Drain the orecchiette, reserving 2/3 cup of the cooking water.
Meanwhile, in a large, deep skillet, heat the olive oil until shimmering. Add the onion and cook over moderately low heat until softened, about 5 minutes. Add the asparagus and crushed red pepper and cook over moderate heat until crisp-tender, about 5 minutes.
Add the orecchiette and the reserved cooking water to the skillet along with the lemon juice and zest season with salt and pepper. Cook, stirring, until the orecchiette is al dente and the asparagus is just tender, about 2 minutes. Add the goat cheese and chives and stir until melted. Transfer the pasta to bowls and serve with Parmesan cheese.