I didn't have a meat thermometer for years, and my mom and grandmothers never did. We just learned by experience.
After you brown the chicken on one side, turn it over, lower the temp just a little, and partially cover skillet with lid. When that side is nicely browned, it should be done. Stick a fork in it and press with spatula. If no pink juice runs out, it's done.
If you do find the chicken is still pink inside when you cut into it, set it on a paper towel in the microwave, cover with another towel, and nuke for 45 seconds or so. Don't overdo it or it will be hard as a brick.
We get by with a little help from our friends