Heat a large saute (fry) pan over medium high heat.
Carefully add the olive oil and let it heat up but don't let it smoke.
Season the trout with salt and pepper and when the oil is hot, add the fillets skin side down and cook for three to four minutes. How long depends on the thickness of of the fish, the type of pan and the amount of heat.
Flip the fillets over and cook for another two to three minutes or until the fish is cooked through and starts to flake. Remove the fish and transfer to a plate and keep warm.
Using your spatula, remove any small pieces of fish that may be stuck to the pan.
Lower the heat to medium, add two tablespoons of butter to the pan and saute the shallots for a couple of minutes.
Add the chopped tomatoes and capers and cook for one an additional minute or two.
Add the lemon juice and bring to a boil. Reduce the sauce by half or until it is thick enough to coat the back of a spoon.
Reduce the heat to low and add the rest of the butter gradually in small pieces, whisking after each addition. Taste and adjust the seasoning with salt and pepper.
Plate the trout, spoon the sauce over the fish and garnish the plate with chives and toasted pine nuts.
Serve with potatoes or rice and your favorite vegetable.