In a normal air/blood mixture, hemoglobin is an unstable molecule that is found either as a compound with oxygen or carbon dioxide. Hemoglobin has an affinity for both molecules and bonds readily with each. However, it will bond more favorably with the molecule that is the greater concentration in the solution, giving up oxygen where carbon dioxide is prevalent (such as in the capilliaries) and giving up carbon dioxide when oxygen is readily available (such as the lungs). As such, in this state, it is rather unstable and prone to change.
However, when hemoglobin bonds with carbon monoxide, it is at a very low energy state and will only give up the carbon monoxide when oxygen is in extremely high concentrations (at higher pressures and concentrations than that of normal air - normally 23% at 15 psi). As such, less hemoglobin becomes available for carrying oxygen through the body, eventually resulting in death by suffocation.
Even at concentrations and pressures typical of a hyperbaric chamber, only about 50% of the carbon monoxide tied to hemoglobin will be removed every 30-60 minutes of treatment. In addition, the chamber must contain some carbon dioxide to prevent hyperventilation.