Airport it self is open 24hrs. A day. The airline counters open at 3:15 and 3:30am. There some different factors that happen at all airports Medford included. I know first hand that yes you should be at the counter or in line at 330am for your 530am departure. Don't forget plane boards 30 minutes prior to departure, and flights are allowed to leave 10 minutes early.
The airport is busy in the mornings, so if you've already checked in online you should arrive about 1 1/2 hours prior to your departure time.
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