Melt the butter in a pot set over medium heat. Add shallot and mushroom and cook 5 minutes. Stir in the flour. While stirring, slowly mix in the stock. Bring to a simmer; simmer 5 minutes. Preheat grill to medium-high.
When the sauce has simmered 5 minutes, stir in the cream, season with salt and pepper, cover and reserve on low heat.
Brush halibut fillets with the olive oil; season with salt and pepper. Brush the grill lightly with oil. Grill fish 3 to 4 minutes per side, or until just cooked through.
Plate the fish, top with the sauce, sprinkle with chives and serve.