Gyalzur was born as Tenzin Dolkar in Shigatse, Tibet. She lost her parents in the Chinese annexation of Tibet and as a child crossed the Himalayas on foot and on horseback to flee to India. She grew up in an Indian orphanage, and was chosen to be one of a dozen children sent to Germany by the Tibetan government in exile in 1963. In Germany, she obtained a nursing degree, married another Tibetan refugee, Losang Gyalzur, and moved with him to Switzerland.