Melt butter in a large skillet over medium heat. Add couscous; cook and stir until slightly toasted, 2 to 3 minutes.

Add chicken broth; bring to a boil. Reduce heat to low; simmer until most broth absorbed and couscous plumped, 6 to 7 minutes.

Stir in heavy cream and pimentos; add cayenne pepper and cook until couscous tender, 2 to 3 minutes, adding more broth if needed.

Off heat, stir in Cheddar cheese until melted; add chives and stir to combine. Season with salt, black pepper, and cayenne pepper.