We report on an all-sky search for periodic gravitational waves in the frequency band 20-475 Hz and with a frequency time derivative in the range of [ -1.0 , +0.1 ] \times 10 ^ { -8 } Hz/s . Such a signal could be produced by a nearby spinning and slightly non-axisymmetric isolated neutron star in our galaxy . This search uses the data from Advanced LIGO ’ s first observational run , O1 . No periodic gravitational wave signals were observed , and upper limits were placed on their strengths . The lowest upper limits on worst-case ( linearly polarized ) strain amplitude h _ { 0 } are \sim 4 \times 10 ^ { -25 } near 170 Hz . For a circularly polarized source ( most favorable orientation ) , the smallest upper limits obtained are \sim 1.5 \times 10 ^ { -25 } . These upper limits refer to all sky locations and the entire range of frequency derivative values . For a population-averaged ensemble of sky locations and stellar orientations , the lowest upper limits obtained for the strain amplitude are \sim 2.5 \times 10 ^ { -25 } .