Recent research has uncovered a fascinating quantum liquid made up solely of electrons confined to a plane surface. Found only at temperatures near absolute zero and in extremely strong magnetic fields, this liquid can flow without friction. The excited states of this liquid consist of peculiar particle-like objects that carry an exact fraction of an electron charge. Called quasiparticles, these excitations can themselves condense into new liquid states. Each such liquid is characterized by a fractional quantum number that is directly observable in a simple electrical measurement. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect.