Place chicken breasts in a pot with broth and bring to a boil over high heat. Turn heat to low, cover and simmer for about 15 to 20 minutes. Do not let the liquid boil off; add water if necessary. To test for if cooked, remove one chicken piece from the pot and cut it in halfâ€”thoroughly cooked meat will be white or light brown all the way through. Strain cooked chicken from pot and place on a cutting board; set aside remaining broth. Allow chicken to cool, then chop into small pieces.
Put chicken pieces and Â˝ cup of leftover broth in a blender or food processor. Puree the meat until texture is smooth, adding up to Â˝ cup more broth as needed. At least once during the puree process, stop the appliance and scrape down the sides of the bowl with a spatula.
Spoon the pureed chicken into ice cube trays and cover with plastic wrap. Freeze for 8 to 10 hours, or overnight.
Once the puree has set, remove trays from freezer; turn them bottom-side up and rinse under hot water for a few moments to loosen the cubes. Pop the cubes from the trays, and place them in a freezer storage bag marked with the word â€śCHICKENâ€ť and the date of preparation. Thaw, warm and serve cubes as needed.