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Ohio State University Center for Cosmology and AstroParticle Physics ; Spanish Ramon y Cajal MICINN program ; Spanish Ministerio de Economia y Competitividad ; Juan de la Cierva fellowship ; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; 'Plan Estatal de Investigacion Cientfica y Tecnica y de Innovacion' program of the Spanish government ; U.S. Department of Energy ; U.S. National Science Foundation ; Ministry of Science and Education of Spain ; Science and Technology Facilities Council of the United Kingdom ; Higher Education Funding Council for England ; National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign ; Kavli Institute of Cosmological Physics at the University of Chicago ; Center for Cosmology and Astro-Particle Physics at the Ohio State University ; Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University ; Financiadora de Estudos e Projetos ; Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) ; Ministerio da Ciencia, Tecnologia e Inovacao ; Deutsche Forschungsgemeinschaft ; Argonne National Laboratory ; University of California at Santa Cruz ; University of Cambridge ; Centro de Investigaciones Energeticas ; Medioambientales y Tecnologicas-Madrid ; University of Chicago ; University College London ; DES-Brazil Consortium ; University of Edinburgh ; Eidgenossische Technische Hochschule (ETH) Zurich ; Fermi National Accelerator Laboratory ; University of Illinois at Urbana-Champaign ; Institut de Ciencies de l'Espai (IEEC/CSIC) ; Institut de Fisica d'Altes Energies ; Lawrence Berkeley National Laboratory ; Ludwig-Maximilians Universitat Munchen ; associated Excellence Cluster Universe ; University of Michigan ; National Optical Astronomy Observatory ; University of Nottingham ; Ohio State University ; University of Pennsylvania ; University of Portsmouth ; SLAC National Accelerator Laboratory ; Stanford University ; University of Sussex ; Texas AM University ; OzDES Membership Consortium ; National Science Foundation ; MINECO ; ERDF funds from the European Union ; CERCA program of the Generalitat de Catalunya ; European Research Council under the European Union ; ERC ; Australian Research Council Centre of Excellence ; U.S. Department of Energy, Office of Science, Office of High Energy Physics ; Spanish Ministerio de Economia y Competitividad: ESP2013-48274-C3-1-P ; CNPq: 465376/2014-2 ; National Science Foundation: AST-1138766 ; National Science Foundation: AST-1536171 ; MINECO: AYA2015-71825 ; MINECO: ESP2015-66861 ; MINECO: FPA2015-68048 ; MINECO: SEV-2016-0588 ; MINECO: SEV-2016-0597 ; MINECO: MDM-2015-0509 ; ERC: 240672 ; ERC: 291329 ; ERC: 306478 ; Australian Research Council Centre of Excellence: CE110001020 ; U.S. Department of Energy, Office of Science, Office of High Energy Physics: DE-AC02-07CH11359 ; We present angular diameter distance measurements obtained by locating the baryon acoustic oscillations (BAO) scale in the distribution of galaxies selected from the first year of Dark Energy Survey data. We consider a sample of over 1.3 million galaxies distributed over a footprint of 1336 deg(2) with 0.6 < z(photo) < 1 and a typical redshift uncertainty of 0.03(1 + z). This sample was selected, as fully described in a companion paper, using a colour/magnitude selection that optimizes trade-offs between number density and redshift uncertainty. We investigate the BAO signal in the projected clustering using three conventions, the angular separation, the comoving transverse separation, and spherical harmonics. Further, we compare results obtained from template-based and machine-learning photometric redshift determinations. We use 1800 simulations that approximate our sample in order to produce covariance matrices and allow us to validate our distance scale measurement methodology. We measure the angular diameter distance, D-A, at the effective redshift of our sample divided by the true physical scale of the BAO feature, r(d). We obtain close to a 4 per cent distance measurement of D-A (z(eff )= 0.81)/r(d) = 10.75 +/- 0.43. These results are consistent with the flat A cold dark matter concordance cosmological model supported by numerous other recent experimental results.