1. Season the chicken halves all over with salt and pepper.
2. Over medium-high heat, heat a saute pan large enough to hold the chicken halves comfortably without overcrowding.
3. When the pan is very hot, add the oil and, when the oil is almost smoking, add the chicken, starting skin side down.
4. Saute the chicken until golden brown on all sides, 7 to 10 minutes total.
5. Add the onion and garlic to the pan with chicken and saute, stirring, for about 2 minutes more.
6. Transfer the chicken halves to a plate and cover with aluminum foil to keep warm.
7. Add the vinegar and the wine to the pan and stir and scrape to deglaze the pan deposits.
8. Bring the liquid to a boil and continue boiling until it has reduced by half its volume.
9. Stir in the tomato and butter and add the bouquet garni.
10. Return the chicken halves to the pan, reduce the heat to maintain a gentle simmer, and continue cooking until the chicken is done, about 20 minutes more.
11. Remove the chicken from the pan again to a clean plate and cover to keep warm.
12. Remove and discard the bouquet garni.
13. With an immersion blender, blend the sauce until smooth.
14. Or carefully transfer the sauce to a blender or processor, in batches if necessary to avoid overcrowding, and very carefully blend until smooth, taking precautions to avoid splattering; then return the sauce to the pan.
15. Taste the sauce and adjust the seasonings with salt and pepper.
16. Return the chicken to the pan, bring the liquid back to a gentle boil, and serve.

Yield: 4 servings