Results are presented from a semicoherent search for continuous gravitational waves from the brightest low-mass X-ray binary, Scorpius X-1, using data collected during the first Advanced LIGO observing run. The search combines a frequency domain matched filter (Bessel-weighted F-statistic) with a hidden Markov model to track wandering of the neutron star spin frequency. No evidence of gravitational waves is found in the frequency range 60650 Hz. Frequentist 95% confidence strain upper limits, h95%0 = 4.0 x 10−25, 8.3 x 10−25, and 3.0 x 10−25 for electromagnetically restricted source orientation, unknown polarization, and circular polarization, respectively, are reported at 106 Hz. They are ≤ 10 times higher than the theoretical torque-balan...