Yes, they do. Chickens that are allowed to free range are less susceptible than penned chickens, but they do get worms. A healthy chicken can carry a small worm load, but when they overwhelm the system, they need to be wormed.
A lot of vets (even ones who won't see chickens) will do a fecal test for around $20. There really isn't any other way until they start to get sick or even die; occasionally you will see worms in poop but certainly not always. Many folks on here worm routinely; it's on my chore list for today.
I'll give you a couple of links to get you started reading on it.