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Using millions of father-son pairs spanning more than 100 years of US history, we find that children of immigrants from nearly every sending country have higher rates of upward mobility than children of the US-born. Immigrants' advantage is similar historically and today despite dramatic shifts in sending countries and US immigration policy. Immigrants achieve this advantage in part by choosing to settle in locations that offer better prospects for their children. These findings are consistent with the "American Dream" view that even poorer immigrants can improve their children's prospects.