The code works, I just forgot to add another parameter ['asyncBlocking'] . This code works very well:
chrome.webRequest.onAuthRequired.addListener( function(details, callbackFn) { console.log("onAuthRequired!", details, callbackFn); callbackFn({ authCredentials: {username: "1", password: "__TestUser"} }); }, {urls: ["<all_urls>"]}, ['asyncBlocking'] );
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