Place fresh salmon in a skillet, skin-side down, and cover with cool water. Bring to a simmer over low-medium heat and gently cook until just short of being cooked all the way through. Remove from heat and allow to sit for a few minutes or until flesh is opaque and flakes easily. Prepare a bed of several layers of paper towels. Remove filet from the water and place on paper towels to soak up excess water; set aside to cool.

Meanwhile, in a medium sized mixing bowl, mash the softened butter until no chunks remain. Whisk in the olive oil and lemon juice until combined, then fold in the smoked salmon, capers and chives. Add chunks of the cooled cooked salmon to the butter mixture, leaving the skin behind, which will be easy. Fold everything together well, taste and season as desired. The rillettes taste best after they have rested for at least 2 hours, but you can also make them 2 days ahead, refrigerated in an airtight container. Bring to room temperature before serving with an array of low FODMAP crudité, crackers and bread.