Place pimento in container of an electric blender and process until smooth, stopping once to scrape down sides. Set pimento aside.
Melt butter in heavy saucepan over low heat; add flour and stir until flour mixture is smooth. Cook 1 minute, stirring constantly.
Add chicken broth and half-and-half gradually to flour mixture, and cook over medium heat, stirring constantly, until broth mixture is thickened and bubbly.
Stir in pimento, onion, salt, and hot sauce; cook over low heat, stirring constantly, until thoroughly heated.