In the gap Hamming distance problem, two parties must
determine whether their respective strings $x,y\in\{0,1\}^n$
are at Hamming distance less than $n/2-\sqrt n$ or greater
than $n/2+\sqrt n.$ In a recent tour de force, Chakrabarti and
Regev (STOC '11) proved the long-conjectured $\Omega(n)$ bound
on the randomized communication complexity of this problem. In
follow-up work several months ago, Vidick (2010; ECCC TR11-051)
discovered a simpler proof. We contribute a new proof, which
is simpler yet and a page-and-a-half long.