Salaam,
There is a difference between Halaal and Zabiha. I think we know what is halaal, pretty much everything except roadkill, pork, and alcohol to put it simply. Everything else is Halaal meat, but Zabiha targets specifically how the animal was slaughtered and if "bismillah" was said.
Just because a market says it is "halaal" doesn't necessarily mean it is Zabiha. And even so, it is SO difficult to regulate and monitor. Just because a place "says so" so don't really know for sure how the slaughter process was done. Maybe is was done in accordance, but the chickens were raised in harsh environments just like the ones at Tyson and other horrible farms. I don't feel ok eating this.
Personally, I hardly ever eat meat because it's such a difficult thing to do ethically/islamically unless you slaughter the meat yourself, or have a trusted friend. If I go to someone's house, I will eat whatever they provide. If I end up buying meat for myself, I eat organic free range and state "Bismillah" before I eat. This is me doing the best I know how given the conditions.