In a large bowl, whisk together the pesto, vinegar, the ¼ teaspoon salt and the pepper. Gradually whisk in the olive oil until smooth.
Bring a large pot of water to a boil over high heat. Add the 2 tablespoons salt and the orzo. Cook, stirring occasionally to prevent sticking, until the pasta is al dente, according to the package instructions. Drain, rinse under cold running water and drain again. Add the orzo to the vinaigrette and toss to coat evenly.
Add the chicken, tomatoes and spinach to the orzo and toss gently to combine, then serve.