In this paper, we propose a novel design of a data center (DC) using free space optical (FSO) technology. The proposed FSO-DC design is based on fixed, non-mechanical, FSO links facilitating the realization of fully connected FSO racks and rows/columns of racks. Each rack becomes a point of intersection of three fully connected sub-networks. We investigate requirements, advantages and challenges of the proposed design. We develop and analyze a switch-free, fully connected FSO rack, present its link budget analysis and validate it by simulation. Results establish the feasibility of a switch-free FSO rack based on the proposed FSO-DC design. A cost estimate for the proposed FSO-DC design is also presented and compared to three well-known conventional DC designs.