Place the salmon on a cutting board, then pat dry with a paper towel. Carefully slice the filet into thick planks. Cut each plank into strips. Rotate the strips and cut them into ¼-inch dice. Place the salmon in a bowl.
Add olive oil, finely diced red onion, chopped capers, Dijon mustard, lemon zest, fresh lemon juice, depending on how acidic you want the tartare, a diced jalapenño (or more, for more heat), and sliced chives. Toss well, then allow to sit before serving. Taste and adjust seasoning, as needed.
You can place the salmon tartare in a bowl for serving or assemble it in a large round mold. Use your hand or the back of a spoon to firmly press the salmon down to fit the mold. Refrigerate until needed, then carefully lift and remove the mold, then serve the tartare with baguette, crackers, chips, or crudité.