Bring a large pot of salted water to a boil and cook noodles according to package directions. Drain well and set aside.
While noodles are cooking, heat olive oil in a medium sauté pan over medium-high heat. Add the sliced chicken breasts and cook 5 minutes. Add orange juice and bring to a boil. Reduce to a simmer and cook 5 to 8 minutes or until slightly reduced. Remove from heat and stir in zest and sesame oil.
In a large bowl, toss soba noodles with chicken and sauce, green onions, orange segments, spinach and salt. Refrigerate for 20 to 30 minutes. Serve chilled or at room temperature.