Is it safe to be on a 7 day course for zithromax for bacterial chest infection (500 mg a day)? Mild fever persists after first 3 days of the course

YES, SAFE. Zithromycin, unless allergic is a good choice for a wide spectrum antibiotic, very commonly used for upper respiratory infections. In addition 500 mg is a quite large dosage. Antibiotics take some time to work. Your wife should just now be turning the corner if it is a bacterial infection suited to this antibiotic. If not, it may be viral or needs a different antibiotic. Good luck!