Preheat your grill to medium-high. Heat the 1 tsp. oil in a small pot set over medium heat. Add the shallot and garlic and cook 1 to 2 minutes. Add the wine, tomato paste and tarragon and simmer until the wine is reduce by half. Add the cream, bring to a simmer, simmer 1 minute, and then remove from the heat.
Brush chicken with the 1 Tbsp. olive oil; season with salt and pepper. Lightly oil the bars of the grill. Grill chicken 4 minutes per side, or until cooked through. When the chicken is almost done, bring the cream sauce back to a simmer and add the seafood. Simmer 3 minutes, until shrimp and crab are heated through, and the lobster is cooked. Season the sauce with salt and pepper.
Plate the chicken, top with sauce, sprinkle with parsley and serve.