Accurately predicting 3D attributes is crucial for monocular 3D object detection (Mono3D), with depth estimation posing the greatest challenge due to the inherent ambiguity in mapping 2D images to 3D space. While existing methods leverage multiple depth cues (e.g., estimating depth uncertainty, modeling depth error) to improve depth accuracy, they overlook that accurate depth prediction requires conditioning on other 3D attributes, as these attributes are intrinsically inter-correlated through the 3D to 2D projection, which ultimately limits overall accuracy and stability. Inspired by Chain-of-Thought (CoT) in large language models (LLMs), this paper proposes MonoCoP, which leverages a Chain-of-Prediction (CoP) to predict attributes sequentially and conditionally via three key designs. First, it employs a lightweight AttributeNet (AN) for each 3D attribute to learn attribute-specific features. Next, MonoCoP constructs an explicit chain to propagate these learned features from one attribute to the next. Finally, MonoCoP uses a residual connection to aggregate features for each attribute along the chain, ensuring that later attribute predictions are conditioned on all previously processed attributes without forgetting the features of earlier ones. Experimental results show that our MonoCoP achieves state-of-the-art (SoTA) performance on the KITTI leaderboard without requiring additional data and further surpasses existing methods on the Waymo and nuScenes frontal datasets.