  The search for the experimental evidence of quantum spin liquid (QSL) states
is critical but extremely challenging, as the quenched interaction randomness
introduced by structural imperfection is usually inevitable in real materials.
YCu$_3$(OH)$_{6.5}$Br$_{2.5}$ (YCOB) is a spin-1/2 kagome Heisenberg
antiferromagnet (KHA) with strong coupling of $\langle J_1\rangle\sim$ 51 K but
without conventional magnetic freezing down to 50 mK $\sim$ 0.001$\langle
J_1\rangle$. Here, we report a Br nuclear magnetic resonance (NMR) study of the
local spin susceptibility and dynamics on the single crystal of YCOB. The
temperature dependence of NMR main-line shifts and broadening can be well
understood within the frame of the KHA model with randomly distributed hexagons
of alternate exchanges, compatible with the formation of a randomness-induced
QSL state at low temperatures. The in-plane spin fluctuations as measured by
the spin-lattice relaxation rates ($1/T_1$) exhibit a weak temperature
dependence down to $T$ $\sim$ 0.03$\langle J_1\rangle$. Our results demonstrate
that the majority of spins remain highly fluctuating at low temperatures
despite the quenched disorder in YCOB.
