Gaze plays a crucial role in revealing human attention and intention, shedding light on the cognitive processes behind human actions. The integration of gaze guidance with the dynamics of hand-object interactions boosts the accuracy of human motion prediction. However, the lack of datasets that capture the intricate relationship and consistency among gaze, hand, and object movements remains a substantial hurdle. In this paper, we introduce the first Gaze-guided Hand-Object Interaction dataset, GazeHOI, and present a novel task for synthesizing gaze-guided hand-object interactions. Our dataset, GazeHOI, features simultaneous 3D modeling of gaze, hand, and object interactions, comprising 479 sequences with an average duration of 19.1 seconds, 812 sub-sequences, and 33 objects of various sizes. We propose a hierarchical framework centered on a gaze-guided hand-object interaction diffusion model, named GHO-Diffusion. In the pre-diffusion phase, we separate gaze conditions into spatial-temporal features and goal pose conditions at different levels of information granularity. During the diffusion phase, two gaze-conditioned diffusion models are stacked to simplify the complex synthesis of hand-object motions. Here, the object motion diffusion model generates sequences of object motions based on gaze conditions, while the hand motion diffusion model produces hand motions based on the generated object motion. To improve fine-grained goal pose alignment, we introduce a Spherical Gaussian constraint to guide the denoising step. In the subsequent post-diffusion phase, we optimize the generated hand motions using contact consistency. Our extensive experiments highlight the uniqueness of our dataset and the effectiveness of our approach.