  The critical behaviour of stacked-triangular antiferromagnets has been
intensely studied since Kawamura predicted new universality classes for
triangular and helical antiferromagnets. The new universality classes are
linked to an additional discrete degree of freedom, chirality, which is not
present on rectangular lattices, nor in ferromagnets. However, the theoretical
as well as experimental situation is discussed controversially, and generic
scaling without universality has been proposed as an alternative scenario. Here
we present a careful investigation of the zero-field critical behaviour of
RbNiCl$_3$, a stacked-triangular Heisenberg antiferromagnet with very small
Ising anisotropy. From linear birefringence experiments we determine the
specific heat exponent $\alpha$ as well as the critical amplitude ratio
$A^+/A^-$. Our high-resolution measurements point to a single second order
phase transition with standard Heisenberg critical behaviour, contrary to all
theoretical predictions. From a supplementary neutron diffraction study we can
exclude a structural phase transition at T$_N$. We discuss our results in the
context of other available experimental results on RbNiCl$_3$ and related
compounds. We arrive at a simple intuitive explanation which may be relevant
for other discrepancies observed in the critical behaviour of
stacked-triangular antiferromagnets. In RbNiCl$_3$ the ordering of the
chirality is suppressed by strong spin fluctuations, yielding to a different
phase diagram, as compared to e.g.\@ CsNiCl$_3$, where the Ising anisotropy
prevents these fluctuations.
