Melt butter in a large Dutch oven over medium-high heat.
Add celery, carrots and onion; cook, stirring occasionally, until slightly softened, about 4 minutes.
Add mushrooms and garlic; cook, stirring occasionally, until most of the liquid from the mushrooms has evaporated, about 4 minutes.
Stir in chicken, broth, lemon juice, dried tarragon, basil, salt and pepper.
Bring to a simmer over high heat.
Stir in rice; cover, and reduce heat to low.
Cook, undisturbed, until the rice is tender, 10 to 12 minutes.
Divide the soup among 6 bowls and top evenly with tarragon leaves.
