Preheat the oven to 325 F.
Heat 1/4 cup of olive oil in a medium sized saucepan over medium-high heat. Reduce the heat to low and cook the onions and chopped thyme, stirring occasionally for 30-35 minutes or until softened and caramelized.
Toss the cherry tomatoes with a good sprinkling of salt and pepper, and the thyme sprigs and spread them in a small, shallow baking pan. Roast for about 30 minutes without stirring or until the tomatoes are slightly blistered.
Bring a large pot of salted water to a boil over medium high heat and cook the pasta according to the package directions. Before draining reserve 1/4 cup of the pasta cooking water.
Drain the pasta and return it to the pot. Add the 2 tablespoons of extra virgin olive oil and then fold in the caramelized onions.
Gently mix the cherry tomatoes with the pasta. Discard the thyme sprigs. Next gently stir in the goat cheese and a little of the pasta water to loosen the pasta, if needed. Stir in the chives season to taste with salt and pepper, and serve right away.