Bring a large saucepan of lightly-salted water to a boil. Cook the linguine in the boiling water until tender but still firm to the bite; about 11 minutes. Drain, reserving about 3/4 cup of the pasta water. Place the drained pasta in a large bowl.
Melt the butter with the olive oil in a large frypan over low heat. Cook the diced onion and white parts of the spring onion in the butter and oil for about 10 minutes.
Stir the green parts of the spring onions, the chicken, thyme and garlic into the onions then continue cooking until the onions are translucent and the chicken is no longer pink in the centre; about 10 minutes more.
Stir the reserved pasta water into the mixture and remove from the heat. Season with salt and pepper. Pour the mixture over the drained pasta and toss to coat. Sprinkle the Parmesan cheese over the pasta and stir.