Heat oil in large nonstick skillet over medium-low heat. Add onion and squash; cook until onion is golden and squash is tender, stirring occasionally, about 25 minutes. Add broth; bring to boil. Add chicken and cook until heated through, about 5 minutes.
Meanwhile, cook pasta in large pot of boiling salted water until pasta is almost tender, about 6 minutes. Add broccoli rabe; boil until broccoli rabe and pasta are just tender, stirring occasionally, about 2 minutes longer. Drain. Return pasta mixture to same pot. Stir in chicken mixture. Season to taste with salt and pepper.