Not unless you count the muscles needed to breathe hard as major burners of calories. Which they surely are not, compared to say, the muscles needed to run hard. Thin air initiates a host of responses in the body. "These include changes in breathing rate, the pH of your blood, the pH of your muscle, and the rate at which you utilize energy," says Lawrence Armstrong, Ph.D., associate professor of kinesiology at the University of Connecticut and author of Performing in Extreme Environments
(Human Kinetics Press, 2000). "You also experience changes in the nervous, endocrine, and cardiovascular system."
While people who live at altitude ultimately come to utilize oxygen better than those who live at sea level (though the steepest performance advantage is said to be for those who train low and sleep high), this does not necessarily translate into a workout that burns more calories.
Putting aside the vagaries of calculating calorie burn in a workout according to standard tables in the first place (because caloric burn is highly individual, the only accurate way to tell if you burned off that PowerBar is via a calculation based on your individual oxygen consumption), chances are you don't burn that many more calories in Denver than you would in San Francisco. But it will feel that way.
"Your ventilation increases," says Armstrong, "but this perception of increased effort doesn't necessarily mean you're expending more energy. The only increase in energy output would be due to the increased work performed by the rib cage and the muscles involved in breathing. Other than that, you may have a breathless feeling but that doesn't mean you are expending more energy. Additional energy output would be a function of workload, but other than the increased work spent breathing, at a higher altitude you still are doing the same amount of work."