It is not sick. Older leaves on Aloes often die back. Your plant is being completely normal.

Echoing what Poly wrote - as it grows new leaves from the center of the rosette, the older leaves die.

I too agree with what you have heard already. My aloe plants ALWAYS shed a bottom leaf or two when they are ready -- and they are ready when new leaves grow from the center. Don't worry -- let it do its thing.