The (sub)millimeter sky contains a vast wealth of information that is both complementary and inaccessible to other wavelengths. Over half the light we receive is observable at millimeter and submillimeter wavelengths, yet we have mapped only a small portion of the sky at sufficient spatial resolution and sensitivity to detect and resolve distant galaxies or star-forming cores within their large- scale environments. For decades, the astronomical community has highlighted the need for a large, high-throughput (sub)millimeter (lambda similar to 0.35-10 mm) single dish. The Atacama Large Aperture Submillimeter Telescope (AtLAST), with its 50-m aperture and 2 degrees maximal field of view, aims to be such a facility. We present here the preliminary design concept for AtLAST, developed through an EU Horizon 2020-funded design study. Our design approach begins with a long lineage of (sub)millimeter telescopes, relies on calculations and simulations to realize the optics, and uses finite element analysis to optimize the conceptual designs for the mechanical structure and subsystems. The demanding technical requirements for AtLAST, set by transformative science goals, have motivated the design effort to combine novel concepts with lessons learned from previous efforts. The result is an innovative rocking chair design with six instrument bays, two of which are mounted on Nasmyth platforms, inside a large receiver cabin. Ultimately, AtLAST aims to achieve a surface accuracy of a <= 20 mu m root mean square half wavefront error, corresponding to the goal of a Ruze efficiency of >50% at 950 GHz. We conclude that a closed-loop metrology of the active primary surface will be required to achieve our surface accuracy goal. In the next phase of the project, we shall prototype and test such a metrology on existing platforms, with the goal of delivering a mature, construction-ready design by the end of this decade.