  The young A0V star HR 4796A is host to a bright and narrow ring of dust,
thought to originate in collisions between planetesimals within a belt
analogous to the Solar System's Edgeworth-Kuiper belt. Here we present high
spatial resolution 880$\mu$m continuum images from the Atacama Large Millimeter
Array. The 80au radius dust ring is resolved radially with a characteristic
width of 10au, consistent with the narrow profile seen in scattered light. Our
modelling consistently finds that the disk is also vertically resolved with a
similar extent. However, this extent is less than the beam size, and a disk
that is dynamically very cold (i.e. vertically thin) provides a better
theoretical explanation for the narrow scattered light profile, so we remain
cautious about this conclusion. We do not detect $^{12}$CO J=3-2 emission,
concluding that unless the disk is dynamically cold the CO+CO$_2$ ice content
of the planetesimals is of order a few percent or less. We consider the range
of semi-major axes and masses of an interior planet supposed to cause the
ring's eccentricity, finding that such a planet should be more massive than
Neptune and orbit beyond 40au. Independent of our ALMA observations, we note a
conflict between mid-IR pericenter-glow and scattered light imaging
interpretations, concluding that models where the spatial dust density and
grain size vary around the ring should be explored.
