Patients with chronic obstructive pulmonary disease (COPD) may be susceptible to impairments in postural control (PC) when exposed to hypoxia at high altitude. This randomized, placebo-controlled, double-blind, parallel-design trial evaluated the effect of preventive acetazolamide treatment on PC in lowlanders with COPD traveling to 3100 m. 127 lowlanders (85 men, 42 women) with moderate to severe COPD, aged 57 ± 8 y, living below 800 m, were randomized to treatment with acetazolamide 375 mg/d starting 24 h before ascent from 760 m to 3100 m and during a 2-day sojourn in a clinic at 3100 m. PC was evaluated at both altitudes with a balance platform on which patients were standing during five tests of 30 s each. The primary outcome was the center of pressure path length (COPL). In the placebo group, COPL significantly increased from (mean ± SD) 28.8 ± 9.7 cm at 760 m to 30.0 ± 10.0 cm at 3100 m (p = 0.002). In the acetazolamide group, COPL at 760 m and 3100 m were similar with 27.6 ± 9.6 cm and 28.4 ± 9.7 cm (p = 0.069). The mean between-groups difference (acetazolamide-placebo) in altitude-induced change of COPL was −0.54 cm (95%CI −1.66 to 0.58, p = 0.289). Multivariable regression analysis confirmed an increase in COPL of 0.98 cm (0.39 to 1.58, p = 0.001) with ascent from 760 to 3100 m, but no significant effect of acetazolamide (0.66 cm, 95%CI −0.25 to 1.57, p = 0.156) when adjusting for several confounders. In lowlanders with moderate to severe COPD, an ascent to high altitude was associated with impaired postural control and this was not prevented by acetazolamide.