Place chicken in a large pot and cover with water. Boil chicken until done. Remove chicken from pot (keep broth in pot), de-bone and shred; set aside. Salt and pepper broth to taste.
In a separate bowl, combine flour and eggs. Add some chicken broth, a little at a time, until the dough comes together.
Roll dough out onto a floured surface to a rectangle that is ¼” thick. Using a knife or pizza cutter, cut dough into 1 ½” by 1 ½” squares.
Bring chicken broth in original pot to a soft boil. Add dumplings a few at a time, stirring occasionally. Once all of the dumplings have been added to the pot, add de-boned and shredded chicken back to the pot.