I have a concrete shower floor where the existing paint is chipped. I would like to repaint it. What is the best way to do this?

First I would sand the surface smooth and then paint the floor with Non-Skid Paint. Check it out at: NO SLIP SKID SAFE SYSTEMS™ - no slip floor finish on floor surfaces like ceramic tiles, masonry, concrete, driveways, garages, stairs, decks, ramps, kitchens, bathrooms, and showers.
Good luck, Tom

Do as Tom advised. One thing I would like to stress: the floor has to be completely dry otherwise paint will peel off in few months. Back to you. Milo