  Supermassive binary black holes (BBHs) on sub-parsec scales are prime targets
for gravitational wave experiments. They also provide insights on close binary
evolution and hierarchical structure formation. Sub-parsec BBHs cannot be
spatially resolved but indirect methods can identify candidates. In 2015 Liu et
al. reported an optical-continuum periodicity in the quasar PSO
J334.2028+01.4075, with the estimated mass and rest-frame period suggesting an
orbital separation of about 0.006 pc (0.7 micro-arcsec). The persistence of the
quasar's optical periodicity has recently been disfavored over an extended
baseline. However, if a radio jet is launched from a sub-parsec BBH, the
binary's properties can influence the radio structure on larger scales. Here,
we use the Very Long Baseline Array (VLBA) and Karl G. Jansky Very Large Array
(VLA) to study the parsec- and kiloparsec-scale emission energized by the
quasar's putative BBH. We find two VLBA components separated by 3.6 mas (30
pc), tentatively identifying one as the VLBA "core" from which the other was
ejected. The VLBA components contribute to a point-like, time-variable VLA
source that is straddled by lobes spanning 8 arcsec (66 kpc). We classify PSO
J334.2028+01.4075 as a lobe-dominated quasar, albeit with an atypically large
twist of 39 deg between its elongation position angles on parsec- and
kiloparsec-scales. By analogy with 3C 207, a well-studied lobe-dominated quasar
with a similarly-rare twist, we speculate that PSO J334.2028+01.4075 could be
ejecting jet components over an inner cone that traces a precessing jet in a
BBH system.
