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In a large saute pan, heat 1 tablespoon of the olive oil over high heat until hot but not smoking.
Season the filets mignons with salt and pepper and add to the hot pan. Sear on both sides until browned nicely, about 2 to 3 minutes on each side, and transfer to oven for about 3 to 4 minutes for rare, 5 to 6 minutes for medium. Remove from oven and let rest.
Drain excess oil from the pan and return to medium heat; add the shallots and saute briefly; add the red wine and thyme and simmer for 1 minute. Add the chicken stock and continue simmering to reduce to 1 cup; remove from heat and swirl in butter. Season with salt and pepper, to taste.
In another large saute pan over high heat, heat the remaining olive oil until hot but not smoking. Season the shrimp with salt and pepper. Saute the shrimp for about 2 minutes on each side and remove from the pan to a plate.
Drain any excess oil from the pan and return to the stove. Deglaze with the white wine and reduce by 1/2. Slowly add butter, stirring to emulsify; finish with the chives. Season with salt and pepper, to taste.
To serve. On each plate arrange 1 filet and 2 shrimp, spoon about 1 tablespoon of the red wine sauce on the filet and spoon about 1 tablespoon of the white wine sauce over the shrimp. Serve warm.