How is a molecule of potassium chloride held together?

Answer 1

Ionically.

The potassium forms the K^+ cation , and the chloride is the Cl^- anion.

Since each has only one charge, but opposite in nature, they are attracted to each other and bond.

The analogy is the North & South poles of a magnet, which attract.

Answer 2

Potassium chloride, like other ionically bonded solids, does not exist as true molecules. A solid piece of potassium chloride is held together by mutual electrical attraction between the potassium cations and the chloride anions within it. Because each anion is attracted more or less equally to at least two cations and each cation is attracted more or less equally to at least two anions, depending on the specific crystal structure of a particular ionic compound, many formula units are required for a stable piece size.