Shuck corn, then stand each ear on its fat end in a deep bowl and slice kernels off ears into bowl. Set aside.
Cut cobs in half and put in a medium saucepan. Add 2 cups water and bring to a boil over medium-high heat. Boil, uncovered, while you prepare the chowder.
Melt butter in a large saucepan over medium heat. Add shallot, potato, and garlic and cook, stirring constantly, until shallots soften, about 2 minutes. Add flour and cook until flour is no longer raw, 2 minutes.
Slowly whisk 1 cup of the corncob water (discard the rest) into pan, then whisk until mixture is free of lumps. Add milk and half-and-half, corn kernels, salt, and pepper and bring to a simmer over medium heat. Cook, stirring, until mixture thickens slightly and potatoes are soft, about 5 minutes.
Meanwhile, cut salmon into 1-in. dice. Add to chowder and cook until salmon is just cooked through, 2 to 3 minutes.
Pour soup into four bowls and sprinkle each with some chives.