Combine the carrots, celery and onions, chicken stock and 2 cups water in a large pot. Bring to a boil over medium-high heat.
Add the orzo and 1/2 teaspoon salt, reduce the heat to a simmer and cook until the vegetables and orzo are tender, about 10 minutes.
Toss the chicken with 1/2 teaspoon salt and a few grinds of pepper, then add to the soup along with the peas. Simmer until the chicken is just cooked through, 3 to 4 minutes. Add the spinach and cook, stirring, until just wilted.
Off the heat, stir in the lemon juice and zest and season with salt and pepper to taste. Divide the soup between 4 pint-size Mason jars.