In the first decades of the 20th century, almost half of the Chinese Americans born in the United States moved to China—a relocation they assumed would be permanent. At a time when people from around the world flocked to the United States, this little-noticed emigration belied America’s image as a magnet for immigrants and a land of upward mobility for all. Fleeing racism, Chinese Americans who sought greater opportunities saw China, a tottering empire and then a struggling...