You can do it on your PC by enabling chrome://flags/#extensions-on-chrome-urls and adding the necessary url, chrome://extensions/, into "matches" in manifest.json but such extension won't be possible to install on a normal browser due to an invalid scheme error.
To avoid the fatal error, don't use manifest.json to inject the content script/style, do it manually in the background or popup script via chrome.tabs.insertCSS or chrome.tabs.executeScript:
chrome://flags: enable Extensions on chrome:// URLs flag 
manifest.json:
"permissions": ["chrome://*/*", "tabs"],
"background": {
    "scripts": ["background.js"]
},
 
background.js:
var chromeURLstylable;
chrome.permissions.contains({origins: ["chrome://*/*"], permissions: ["tabs"]}, function(state) {
    chromeURLstylable = state;
    console.log("chrome:// urls support", state);
    if (chromeURLstylable) {
        chrome.tabs.onUpdated.addListener(function(tabId, info, tab) {
            if (info.status == "loading" && tab.url.indexOf("chrome://") == 0) {
                chrome.tabs.insertCSS({
                    file: "style.css", 
                    runAt: "document_start",
                    allFrames: true
                });
            }
        });
    }
});
 
Beware of possible problems submitting such extension to the Chrome Webstore.