How to cook chicken on a gas stove top?

The gas stove is not the issue. I think Windischgirl has perhaps touched on your issue. Boneless breasts cook quickly and can easily be overcooked and dry. Checkout some recipes with suggested temp settings and timings. Maybe try a stir fry where you might have more confidence in the chicken being done with just a few minutes of cooking.

If it's on the bone or dark meat, cook it on low heat and slowly.
If it's boneless chicken breast, pound it thin ( or slice it into thin slabs) and cook quickly over high heat for just 3-4 minutes . Use a thermometer to test for doneness, 160F.

I like to dry-brine my chickens first with salt overnight in the fridge, loosely covered. Next day, you can brown it first on medium to medium high, remove to a dish temporarily, drain off some of the fat, sauté aromatics in the remaining rendered fat (onion, garlic and/or celery, carrots, bay leaf, or whatever your recipe calls for), then add liquids (wine, water, stock, and/or tomatoes, any herbs your recipe calls for), bring to a boil, simmer a little, then add back the chicken parts and simmer on low, covered, until done. The liquids and low simmering temp should keep it tender.