Most existing point cloud detection models require large-scale, densely annotated datasets. They typically underperform in domain adaptation settings, due to geometry shifts caused by different physical environments or LiDAR sensor configurations. Therefore, it is challenging but valuable to learn transferable features between a labeled source domain and a novel target domain, without any access to target labels. To tackle this problem, we introduce the framework of 3D Contrastive Co-training (3D-CoCo) with two technical contributions. First, 3D-CoCo is inspired by our observation that the bird-eye-view (BEV) features are more transferable than low-level geometry features. We thus propose a new co-training architecture that includes separate 3D encoders with domain-specific parameters, as well as a BEV transformation module for learning domain-invariant features. Second, 3D-CoCo extends the approach of contrastive instance alignment to point cloud detection, whose performance was largely hindered by the mismatch between the fictitious distribution of BEV features, induced by pseudo-labels, and the true distribution. The mismatch is greatly reduced by 3D-CoCo with transformed point clouds, which are carefully designed by considering specific geometry priors. We construct new domain adaptation benchmarks using three large-scale 3D datasets. Experimental results show that our proposed 3D-CoCo effectively closes the domain gap and outperforms the state-of-the-art methods by large margins.