From a Church News article on the history of the LDS church in Japan

As of January 1, 2009: The Estimated population of Japan was 127 million. There were  123,245 members of the LDS Church - .1% of the population, or one in 1,031.

The history of the Church in Japan dates back to the turn of the 20th Century when Elder Heber J. Grant of the Quorum of the Twelve and 3 missionaries arrived on 12 August 1901.

Under Elder Grant's direction the first Church mission in Asia was established with headquarters in Tokyo. 

Alma Taylor began translating the Book of Mormon into Japanese in 1904 and continued that work for more than five years while he served as president of the Japanese Mission. 

The first meetinghouse in Asia, housing the Tokyo North Branch, was dedicated by Elder Gordon B. Hinckley. The Tokyo Temple was the first temple in Asia and the first in a non-Christian country.