  Low-energy quasiparticle (QP) excitations in the heavy-fermion superconductor
URu$_2$Si$_2$ were investigated by specific-heat $C(T, H, \phi, \theta)$
measurements of a high-quality single crystal. The occurrence of QP excitations
due to the Doppler-shift effect was detected regardless of the field direction
in $C(H)$ of the present clean sample, which is in sharp contrast to a previous
report. Furthermore, the polar-angle-dependent $C(\theta)$ measured under a
rotating magnetic field within the ac plane exhibits a shoulder-like anomaly at
$\theta \sim 45$ deg and a sharp dip at $\theta = 90$ deg ($H \parallel a$) in
the moderate-field region. These features are supported by theoretical analyses
based on microscopic calculations assuming the gap symmetry of $k_z(k_x+ik_y)$,
whose gap structure is characterized by a combination of a horizontal line node
at the equator and point nodes at the poles. The present results have settled
the previous controversy over the gap structure of URu$_2$Si$_2$ and have
authenticated its chiral $d$-wave superconductivity.
