In a medium saucepan, bring the barley and chicken broth to a boil over high heat; reduce the heat and simmer, uncovered, until the barley is tender, about 20 minutes. Drain off any excess liquid. Transfer to a medium bowl and let cool.
While the barley is cooking, in a large nonstick skillet, cook the bacon over medium-high heat until crisp, about 4 minutes. Reserve the fat from the bacon for cooking the burgers. Finely chop the bacon and add to the cooled barley. Mix in the egg, bread crumbs and cheese. Combine thoroughly and score into 4 equal pieces. Wet your hands and form the pieces into patties.
Reheat the bacon fat and cook the burgers over medium heat for 4 minutes on each side.