The purpose of this study is to test whether a oral micronized progesterone reduces the Vasomotor Symptom Score comprised of the number and severity of hot flushes and night sweats in perimenopausal women. Oral micronized progesterone is molecularly identical to human progesterone, a steroid hormone. It is sold by prescription for use to prevent endometrial cancer in women taking estrogen in menopause. This research study will test whether progesterone reduces perimenopausal hot flushes and night sweats. It will also test whether progesterone improves sleep disturbances and anxiety.