Health insurance and chronic illnesses?

In the UK, Private Health Insruance does not cover chronic ilnesses, but the state healthcare does. In the US where there is lately private medical care (aside from that for the poor or groups such as veterans) how do health insurance plans treaty with chronic illnesses including ongoing medication?
Answers:
I have to take-home pay a premium every month for the insurance and a co- pay on the medications- depending on if its generic or name brand. $15.00 for a 30 supply of generic or an 80/20 split on label brands. A lot has to do with the which insurance company one uses.


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