Place chicken in a pot and add enough water to fully cover it. Add salt and a splash of vinegar, then bring to a boil. Cook until the chicken is fully done.
Let the chicken cool completely, then shred it very finely. For the best texture, use a stand mixer or handheld beater — it creates a smoother, creamier filling than hand-shredding.
In a large bowl, combine the shredded chicken with mayonnaise, sour cream, and the remaining ingredients. Mix until everything is well combined. Taste and adjust salt, pepper, or chilli sauce if needed.
Spread a generous layer of the chicken filling on a slice of fresh bread. Top with another slice, then trim off the crusts if desired.
Cut the sandwiches diagonally into halves or quarters. Serve immediately, or cover with cling wrap and refrigerate if serving later to keep the bread soft and moist.