Ashley Wagner, who was controversially named to the 2014 Olympic team, again finished fourth and was selected first alternate.
Both Tennell, 19, and Chen, 18, will be participating in their first Olympics.
Nagasu, 24, competed in the 2010 Vancouver Games, finishing fourth.
Wagner, 26, the only U.S. woman to win a world championship medal in the past 11 seasons, was upset by the judging at the U.S. nationals.
"I'm furious," the 2016 world silver medallist told reporters. "I am absolutely furious. I know when I go and I lay it down and I absolutely left one jump on the table (turning a triple salchow into a single) but for me to put out two programmes that I did at this competition, as solid as I skated and to get those scores, I am furious, and I think deservedly so."
The 2018 Winter Games will take place Feb. 9-25 in Pyeongchang, South Korea.
U.S. Figure Skating will announce its men's, pairs and ice dance athletes on Sunday after the men's and pairs competition the previous day.
(Reporting by Gene Cherry in Wilson, North Carolina; Editing by Christian Radnedge)
