There is an extension called OpenHere that will do this. It will add the option in the right click context menu Open in This Window. Just right clcik on the link you want to open in the same tab.

Edit in response to comment:

You can do it with AutoHotkey. You have need to download it and install it on your PC. After that just copy the code below and save it with a .ahk extension.

SetTitleMatchMode, RegEx
#IfWinActive, - Google Chrome$
!RButton::  
    !LButton::  
        KeyWait, Alt  
        Click, Right  
        SendInput, e  
        ControlFocus, Chrome_OmniboxView1  
        SendInput, ^a{Backspace}  
        SendInput, ^v{Enter}   
        return
#IfWinActive

Now when you press Alt + LClick, it will copy the link to the clipboard and past it in the address bar of Chrome. Just press the button and click and release with the click and the link will open in the same tab.

I believe that chrome does not allow the popups to open an external page by any way. The only solution I know is to place an iframe in your popup.html file with src attribute set to popup2.html and place all your html inside popup2.html. However, consider that all websites do not work well inside iframe.

If you are trying to open url in currently active tab then try following:

Attach following script to your popup.html file:

var hrefs = document.getElementsByTagName("a");

function openLink() {
    var href = this.href;
    chrome.tabs.query({active: true, currentWindow: true}, function(tabs) {
        var tab = tabs[0];
        chrome.tabs.update(tab.id, {url: href});
    });
}

for (var i=0,a; a=hrefs[i]; ++i) {
    hrefs[i].addEventListener('click', openLink);
}

You need to add tabs permisson to your manifest file for this to work.

Installing the "Open PinnedTab Link" Chrome extension with the settings below and restarting the browser helped to solve this problem. Links clicked within the same domain inside a pinned tab open in the same tab whereas external links open in a new tab.

• Enabled: Clicked links will open in new tabs. - OFF
• Outbound Links Only: Keep links to the same domain in the pinned tab. - ON