In a large pot, bring water to a boil. Add generous amount of salt and chicken breasts. Let boil until done (about 10-15 minutes). Drain, reserving 1/2 C of the chicken broth, and let chicken cool.
While chicken is boiling and cooling, prepare pasta and sauce.
Add pasta to a large pot of salted boiling water and cook just until al dente. Drain and rinse when finished. Set aside.
To prepare sauce, pour undrained tomatoes & greens chiles into a medium sauce pan over medium heat. Add broth. Cube the Velveeta cheese & add to tomatoes and broth. Stir until cheese melts. Do not let scorch. When cheese is melted, add sour cream. Stirring constantly again. Add salt, peppers and garlic. Stir again. Remove from heat.
Shred cooled chicken and add to sauce. Return 1/2 of pasta to its pot. Pour sauce over pasta and toss in pot. Add rest of pasta and toss well again. Serve in pot or transfer to a large casserole dish to be served.