The battle between the US and China over computer-chip makers has expanded to a new front: the companies that test the technology. Citing national-security concerns, a US semiconductor-testing company, Cohu Inc. is mounting a quiet campaign to derail the planned $580 million sale of an American rival, Xcerra Corp., to a Chinese state-backed group, according to documents reviewed by The Wall Street Journal. The US government has previously shot down attempts by Chinese interests to buy makers of the chip technology used in mobile phones, military equipment and other systems. The deal for Xcerra, which provides equipment to test chips but doesn’t actually make them, could test how far the Trump administration is willing to go to shut China out of the sensitive sector at the heart of a trade battle. Chinese officials and executives say the national security concerns their US counterparts raise are a pretext and that the US is simply trying to stave off competition.