According to The Mathematics Genealogy Project,

Leonhard Euler

Ph.D. Universitšt Basel 1726
 

had a student

Joseph Louis Lagrange

Ph.D.

who had a student

Simeon Denis Poisson

Ph.D.

who had a student

Michel Chasles

Ph.D. …cole Polytechnique 1814
 

who had a student

H. A. (Hubert Anson) Newton

B.S. Yale University 1850
 

who had a student

E. H. (Eliakim Hastings) Moore

Ph.D. Yale University 1885
 

who had a student

George David Birkhoff

Ph.D. University of Chicago 1907
 

who had a student

H. C. Marston (Harold Calvin) Morse

Ph.D. Harvard University 1917
 

who had a student

Gustav Arnold Hedlund

Ph.D. Harvard University 1930
 

who had a student

Walter Helbig Gottschalk

Ph.D. University of Virginia 1944
 

who had a student

Hsin Chu

Ph.D. University of Pennsylvania 1959
 

who had a student

William Jesse Gray

Ph.D. University of Alabama-Tuscaloosa 1965
 

who had a student

William Thomas Trotter, Jr.

Ph.D. University of Alabama-Tuscaloosa 1968
 

who is my Ph.D. thesis advisor.