  Short distance scaling limits of a class of integrable models on
two-dimensional Minkowski space are considered in the algebraic framework of
quantum field theory. Making use of the wedge-local quantum fields generating
these models, it is shown that massless scaling limit theories exist, and
decompose into (twisted) tensor products of chiral, translation-dilation
covariant field theories. On the subspace which is generated from the vacuum by
the observables localized in finite light ray intervals, this symmetry can be
extended to the M\"obius group. The structure of the interval-localized
algebras in the chiral models is discussed in two explicit examples.
