Prepare rice according to directions listed on package.
Halfway through the rice cooking, in a separate large pot, melt 1 Tbsp butter over medium heat. Add onion, carrots and celery and saute 4 minutes, add garlic and saute 30 seconds longer.
Add chicken broth, thyme, marjoram, sage, rosemary and season with salt and black pepper to taste. Increase heat to medium-high, add chicken and bring mixture to a boil.
Cover pot with lid, reduce to medium-low heat and allow mixture to simmer until chicken is cooked through, about 12 – 16 minutes (rotating chicken to opposite side once during cooking for thicker chicken breasts – if they don’t fully immerse in broth).
Remove chicken and set aside on cutting board to cool 5 minutes then shred into small bite size pieces. Leave soup covered over warm heat.
Meanwhile in a separate medium saucepan, melt remaining 6 Tbsp butter over medium heat. Add flour and cook 1 1/2 minutes, whisking constantly.
Then while whisking vigorously, slowly pour milk into butter/flour mixture. Whisk in heavy cream. Cook mixture, stirring constantly until it thickens.
Add milk mixture to soup mixture in pot along with shredded chicken, cooked rice, and lemon zest. Stir well and remove from heat.