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Segmentation of infected areas in chest CT volumes is of great significance for further diagnosis and treatment of COVID-19 patients. Due to the complex shapes and varied appearances of lesions, a large number of voxel-level labeled samples are generally required to train a lesion segmentation network, which is a main bottleneck for developing deep learning based medical image segmentation algorithms. In this paper, we propose a weakly-supervised lesion segmentation framework by embedding the Generative Adversarial training process into the Segmentation Network, which is called GASNet. GASNet is optimized to segment the lesion areas of a COVID-19 CT by the segmenter, and to replace the abnormal appearance with a generated normal appearance by the generator, so that the restored CT volumes are indistinguishable from healthy CT volumes by the discriminator. GASNet is supervised by chest CT volumes of many healthy and COVID-19 subjects without voxel-level annotations. Experiments on three public databases show that when using as few as one voxel-level labeled sample, the performance of GASNet is comparable to fully-supervised segmentation algorithms trained on dozens of voxel-level labeled samples.