Channel pruning has been broadly recognized as an effective technique to reduce the computation and memory cost of deep convolutional neural networks. However, conventional pruning methods have limitations in that: they are restricted to pruning process only, and they require a fully pre-trained large model. Such limitations may lead to sub-optimal model quality as well as excessive memory and training cost. In this paper, we propose a novel Channel Exploration methodology, dubbed as CHEX, to rectify these problems. As opposed to pruning-only strategy, we propose to repeatedly prune and regrow the channels throughout the training process, which reduces the risk of pruning important channels prematurely. More exactly: From intra-Layer's aspect, we tackle the channel pruning problem via a well-known column subset selection (CSS) formulation. From inter-Layer's aspect, our regrowing stages open a path for dynamically re-allocating the number of channels across all the layers under a global channel sparsity constraint. In addition, all the exploration process is done in a single training from scratch without the need of a pre-trained large model. Experimental results demonstrate that CHEX can effectively reduce the FLOPs of diverse CNN architectures on a variety of computer vision tasks, including image classification, object detection, instance segmentation, and 3D vision. For example, our compressed ResNet-50 model on ImageNet dataset achieves 76% top-l accuracy with only 25% FLOPs of the original ResNet-50 model, outperforming previous state-of-the-art channel pruning methods. The checkpoints and code are available at here.