  We introduce a sigma model lagrangian generalising a number of new and old
models which can be thought of as chiral, including the Schild string,
ambitwistor strings, and the recently introduced tensionless AdS twistor
strings. This "chiral sigma model" describes maps from a $p$-brane worldvolume
into a symplectic space and is manifestly diffeomorphism- and Weyl-invariant
despite the absence of a worldvolume metric. Construction of the
Batalin-Vilkovisky master action leads to a BRST operator under which the
gauge-fixed action is BRST-exact; we discuss whether this implies that the
chiral brane sigma model defines a topological field theory.
