  We present the ground state properties of a new quantum antiferromagnet
YbBO$_3$ in which the isotropic Yb$^{3+}$ triangular layers are separated by a
non-magnetic layer of partially occupied B and O(2) sites. The magnetization
and heat capacity data establish a spin-orbit entangled effective spin $J_{\rm
eff} = 1/2$ state of Yb$^{3+}$ ions at low temperatures, interacting
antiferromagnetically with an intra-layer coupling $J/k_{\rm B} \simeq 0.53$ K.
The absence of oscillations and a $1/3$ tail in the zero-field muon asymmetries
rule out the onset of magnetic long-range-order as well as spin-freezing down
to 20~mK. An anomalous broad maximum in the temperature dependent heat capacity
with a unusually reduced value and a broad anomaly in zero-field muon
depolarization rate centered at $T^*\simeq 0.7 \frac{J}{k_{\rm B}}$ provide
compelling evidence for a wide fluctuating regime ($0.182 \leq T/J \leq 1.63$)
with slow relaxation. We infer that the fluctuating regime is a universal
feature of a highly frustrated triangular lattice antiferromagnets while the
absence of magnetic long-range-order is due to perfect two-dimensionality of
the spin-lattice protected by non-magnetic site disorder.
