We report on an all-sky search for periodic gravitational waves in the frequency band 20–475 Hz andwith a frequency time derivative in the range of (−1.0, +0.1) × 10−8 Hz=s. Such a signal could be producedby a nearby spinning and slightly nonaxisymmetric isolated neutron star in our galaxy. This search uses thedata from Advanced LIGO’s first observational run, O1. No periodic gravitational wave signals wereobserved, and upper limits were placed on their strengths. The lowest upper limits on worst-case (linearlypolarized) strain amplitude h0 are ∼4 × 10−25 near 170 Hz. For a circularly polarized source (mostfavorable orientation), the smallest upper limits obtained are ∼1.5 × 10−25. These upper limits refer to allsky locations and the entire range of frequency derivative values. For a population-averaged ensemble ofsky locations and stellar orientations, the lowest upper limits obtained for the strain amplitude are∼2.5 × 10−25.