Place potatoes in a steamer and steam until tender but not mushy, 18-20 minutes. Cool, then halve.
Using the small side of a melon baller, carefully scoop out the centers of the potato halves and discard or reserve for another use.
Combine trout, mayonnaise, sour cream, lemon juice, and chives in a bowl.
Place potato halves on a large plate or platter. Scoop about 1 1/2 teaspoons trout mixture into each hollowed-out potato half and sprinkle with some chopped chives.