In a large skillet, heat oil and butter over medium heat.
Add onions and cook, stirring frequently, until golden brown, about 5 minutes.
Season chicken breasts with salt and pepper.
Add them to the skillet and cook for 4 minutes on each side, or until golden brown on the outside and cooked through on the inside.
Remove chicken from the skillet with a slotted spatula and transfer to a platter.
Cover to keep warm.
Add minced garlic to the skillet and cook over low heat for 2 minutes, or until the garlic just releases its fragrance.
Pour in the tawny port and boil for 1 minute, or until reduced to 1/2 cup.
Stir in the heavy cream and boil for an additional 30 seconds, or until the sauce is lightly thickened.
To serve, cut each chicken breast on the diagonal into 1-inch slices.
Pour the sauce over the chicken and garnish with chopped parsley.
Notes / Tips / Wine Advice:
Wine Pairing:
Serve this elegant dish with a dry red wine, such as Cabernet Sauvignon. The Cabernet Sauvignon Sequoia Grove Vineyards 1986 from Napa Valley would be an excellent choice.