The primary objective of this clinical trial is to determine the optimal dose of Gabapentin ER in reducing the number and severity of hot flashes in postmenopausal women. Patients will be randomly assigned to Gabapentin ER or placebo, with a 1 in 4 chance of getting placebo. The total study investigational treatment duration after screening and baseline will be 13 weeks. The primary endpoint of the trial is to compare the number and severity of hot flashes during the investigational treatment compared to baseline. Sleep quality will also be evaluated.