  We describe a class of six-dimensional conformal field theories that have
some properties in common with and possibly are related to a subsector of the
tensionless string theories. The latter theories can for example give rise to
four-dimensional $N = 4$ superconformal Yang-Mills theories upon
compactification on a two-torus. Just like the tensionless string theories, our
theories have an $ADE$-classification, but no other discrete or continuous
parameters. The Hilbert space carries an irreducible representation of the same
Heisenberg group that appears in the tensionless string theories, and the
`Wilson surface' observables obey the same superselection rules. When
compactified on a two-torus, they have the same behaviour under $S$-duality as
super Yang-Mills theory. Our theories are natural generalizations of the
two-form with self-dual field strength that is part of the world-volume theory
of a single five-brane in $M$-theory, and the $A_{N - 1}$ theory can in fact be
seen as arising from $N$ non-interacting chiral two-forms by factoring out the
collective `center of mass' degrees of freedom.
