  We demonstrate that the new single crystal of
YCu$_3$[OH(D)]$_{6.5}$Br$_{2.5}$ (YCOB) is a kagome Heisenberg antiferromagnet
(KHA) without evident orphan spins ($\ll$ 0.8\%). The site mixing between polar
OH$^-$ and non-polar Br$^-$ causes local distortions of Cu-O-Cu exchange paths,
and gives rise to 70(2)\% of randomly distributed hexagons of alternate bonds
($\sim$ $J_1-\Delta J$ and $J_1+\Delta J$) and the rest of almost uniform
hexagons ($\sim$ $J_1$) on the kagome lattice. Simulations of the random
exchange model with $\Delta J$/$J_1$ = 0.7(1) show good agreement with the
experimental observations, including the weak upturn seen in susceptibility and
the slight polarization in magnetization. Despite the average antiferromagnetic
coupling of $J_1$ $\sim$ 60 K, no conventional freezing is observed down to $T$
$\sim$ 0.001$J_1$, and the raw specific heat exhibits a nearly quadratic
temperature dependence below 1 K $\sim$ 0.02$J_1$, phenomenologically
consistent with a gapless (spin gap $\leq$ 0.025$J_1$) Dirac quantum spin
liquid (QSL). Our result sheds new light on the theoretical understanding of
the randomness-relevant gapless QSL behavior in YCOB, as well as in other
relevant materials.
