I have been told that people can get sick from eating chickens that have developed resistance to antibiotics

False. There are many people who believe that antibiotic-resistant bacteria are transferred from animals to humans, but for this to happen a very complex and very rare sequence of events would have to occur. On the contrary, antibiotic resistance of bacteria in humans mainly arises after direct intake of such drugs for the treatment of diseases. This is why their use should be limited to cases where it is strictly necessary, under the supervision of the treating physician.