  Rapidly spinning neutron stars are promising sources of persistent,
continuous gravitational waves. Detecting such a signal would allow probing of
the physical properties of matter under extreme conditions. A significant
fraction of the known pulsar population belongs to binary systems. Searching
for unknown neutron stars in binary systems requires specialized algorithms to
address unknown orbital frequency modulations. We present a search for
continuous gravitational waves emitted by neutron stars in binary systems in
early data from the third observing run of the Advanced LIGO and Advanced Virgo
detectors using the semicoherent, GPU-accelerated, BinarySkyHough pipeline. The
search analyzes the most sensitive frequency band of the LIGO detectors, 50 -
300 Hz. Binary orbital parameters are split into four regions, comprising
orbital periods of 3 - 45 days and projected semimajor axes of 2 - 40
light-seconds. No detections are reported. We estimate the sensitivity of the
search using simulated continuous wave signals, achieving the most sensitive
results to date across the analyzed parameter space.
