In the bowl of a stand mixer fitted with the dough hook (or large bowl), combine 3 large eggs, 2 cups unbleached all-purpose flour, and a pinch of salt.
Mix slowly, adding water a little at a time until the dough comes together but is not sticky; if dough is too wet add a bit more flour.
Remove the dough, place it on a lightly floured cutting board, cover with a bowl, and let rest for 10 minutes.
Feed the rested dough through a pasta machine following the manufacturer's directions, rolling to progressively thinner settings until you reach a setting suitable for long pasta (about setting 6 on a KitchenAid roller).
Prepare a large pot of salted boiling water and cook the spaghetti rigati until al dente according to thickness, then drain.
Meanwhile, in a skillet cook the chicken in the tomato sauce over medium heat until the chicken is fully cooked and the sauce is heated through.
Toss the cooked pasta with the chicken and tomato sauce and serve immediately.