Step 1Slice the salmon on a diagonal into 8 equal pieces about 1/2 inch thick (or have it cut at the fish market). Season the slices lightly on both sides with salt and pepper. Heat the oil in a large nonstick skillet over medium-high heat and cook the salmon slices until just slightly underdone, about 1 1/2 minutes per side. Transfer the filets to warm plates.
Step 2Add the cucumber to the skillet and cook it over medium heat until lightly browned, 2 to 3 minutes. Add the butter, a dash of salt and the lemon juice and cook until the butter browns slightly, 4 minutes. Remove the pan from the heat, arrange the cucumbers alongside the salmon and drizzle the browned butter over the fish. Garnish the fish with chives.