  We provide an alternative proof that the Chow group of $1$-cycles on a
Severi--Brauer variety associated to a biquaternion division algebra is
torsion-free. There are three proofs of this result in the literature, all of
which are due to Karpenko and rely on a clever use of $K$-theory. The proof
that we give here, by contrast, is geometric and uses degenerations of quartic
elliptic normal curves.
