Bring water to a boil in a large saucepan or soup pot. You're going to want quite a bit more than the amount of chicken, to make sure it can cook the meat. 

Once the water has come to a boil, add some salt (like you would for pasta water) and the chicken breasts.  Remove from the heat and cover with a lid.

Let sit, covered, for 20-25 minutes.  Then check the internal temp of the chicken at the fattest part...it should read at least 145 F (it probably won't go much above that).  

If it's reached that temp, it's done.  If not, drain some of the water and add some more boiling water (again, the electric kettle is super helpful), leaving it sit with the lid on for another 5-10 minutes.

Once it's reached 145 F inside, drain the water.

Place the chicken breasts in your stand mixer with the paddle attachment. 

Turn the mixer on very low and gradually bump it up a couple notches as the chicken is shredded.  It will take about 10 seconds total. 

I give it a few medium-speed pulses right at the end to really break things up.