This paper proposes a novel three-dimensional (3D) near-field beamforming (BF) design for Large Intelligent Surfaces (LIS). The key contributions include: (1) defining the near-field and far-field regions of LIS, and showing that the Fresnel near-field region, where phase variations dominate, can be significantly enlarged by considering imperfect 2D far-field BF. (2) Decomposing the optimal 3D-BF into a 2D far-field BF and a 1D near-field BF, which reduces codebook size and is compatible with existing 5G-NR systems. (3) Analyzing an optimal codebook design for the 1D near-field BF, showing that a small codebook can perform close to optimal. Numerical results demonstrate that the proposed 2D+1D BF design effectively recovers array-gains in the near-field of LIS. The paper also discusses the differences between near-field and far-field regions of LIS, the impact of UE location on near-field BF, and the decomposition theorem that allows 3D-BF to be implemented in a simpler form. The proposed design is practical, efficient, and compatible with existing systems.This paper proposes a novel three-dimensional (3D) near-field beamforming (BF) design for Large Intelligent Surfaces (LIS). The key contributions include: (1) defining the near-field and far-field regions of LIS, and showing that the Fresnel near-field region, where phase variations dominate, can be significantly enlarged by considering imperfect 2D far-field BF. (2) Decomposing the optimal 3D-BF into a 2D far-field BF and a 1D near-field BF, which reduces codebook size and is compatible with existing 5G-NR systems. (3) Analyzing an optimal codebook design for the 1D near-field BF, showing that a small codebook can perform close to optimal. Numerical results demonstrate that the proposed 2D+1D BF design effectively recovers array-gains in the near-field of LIS. The paper also discusses the differences between near-field and far-field regions of LIS, the impact of UE location on near-field BF, and the decomposition theorem that allows 3D-BF to be implemented in a simpler form. The proposed design is practical, efficient, and compatible with existing systems.