We report high-resolution measurements of the specific heat of the hex
agonal antiferromagnet CsCuCl3 with ferromagnetically coupled Cu2+ cha
ins in magnetic fields parallel to the hexagonal axis. The zero-field
data can be described assuming a second-order phase transition with a
chiral XY critical exponent alpha near 0.35, except very close to the
Neel temperature where the transition seems to be of weakly first orde
r. This might be an indication for the failure of XY chiral universali
ty. The previously observed first-order transition from an ''umbrella'
' to a coplanar spin structure at high fields merges the transition li
ne to the paramagnet in a multicritical point (T-c = 10.59 K, B-m = 5.
5 T). The transition to the new coplanar structure from the saturated
paramagnetic phase above B-m seems, rather unexpectedly, also to be de
scribable as a second-order transition with alpha approximate to 0.23.