  I analyze the one-dimensional, cubic Schr\"odinger equation, with
nonlinearity constructed from the current density, rather than, as is usual,
from the charge density. A soliton solution is found, where the soliton moves
only in one direction. Relation to higher-dimensional Chern--Simons theory is
indicated. The theory is quantized and results for the two-body quantum problem
agree at weak coupling with those coming from a semiclassical quantization of
the soliton.
