Heat olive oil in small saucepot over low heat with crushed garlic cloves for 3-4 minutes. Remove from the heat and reserve.
Split open the French bread lengthwise, brush both cut sides liberally with the garlic oil and place under the broiler to toast until golden brown. Remove and chop the bread into extra-large, bite-sized pieces.
In a pot add onion, chicken broth and the crushed tomatoes. Bring the mixture up to a simmer.
While the tomatoes are getting hot, chop the poached chicken into chunks. Once the tomatoes are simmering, add the chunked chicken, chopped tarragon and season with a little salt and pepper.
Continue to simmer until the chicken is heated through.
Divide the garlic bread chunks between 4 serving bowls, top with stew and serve.