  Specific heat has been measured in FeSe single crystals down to 0.414 K under
magnetic fields up to 16 T. A sharp specific heat anomaly at about 8.2 K is
observed and is related to the superconducting transition. Another jump of
specific heat is observed at about 1.08 K which may either reflect an
antiferromagnetic transition of the system or a superconducting transition
arising from Al impurity. We would argue that this anomaly in low temperature
region may be the long sought antiferromagnetic transition in FeSe. Global
fitting in wide temperature region shows that the models with a single
contribution with isotropic s-wave, anisotropic s-wave, and d-wave gap all do
not work well, nor the two isotropic s-wave gaps. We then fit the data by a
model with two components in which one has the gap function of
$\Delta_0(1+\alpha cos2\theta)$. To have a good global fitting and the entropy
conservation for the low temperature transition, we reach a conclusion that the
gap minimum should be smaller than 0.15 meV ($\alpha$ = 0.9 to 1), indicating
that the superconducting gap(s) are highly anisotropic. Our results are very
consistent with the gap structure derived recently from the scanning tunneling
spectroscopy measurements and yield specific heat contributions of about 32\%
weight from the hole pocket and 68\% from the electron pockets.
