Season chicken breasts with salt and pepper. Combine parmesan cheese and italian bread crumbs. Mix egg with small amount of water and dip chicken breasts in egg and then in the crumb mixture.
In pan on medium heat, melt 2 Tbsp butter and 1 Tbsp olive oil and saute chicken breasts for approximately 10 minutes each side. Remove chicken breasts and keep warm under tin foil. Add remaining butter and olive oil to same pan. Add garlic, saute for 2 minutes, add tomato sauce, tomato paste and simmer for 10 minutes. Remove from heat and add the vermouth and cream. Serve chicken with sauce poured over, sprinkle chives on top and serve on any kind of cooked pasta.