Had to do this myself as their new download statusbar finally kicked in on my computer making it look a bit too much like Firefox. I first tried Download Statusbar which is an extension for Chrome that works but not like the original. I see a lot of people hate the new statusbar which appears to have launched in February and even though I've done updates since then, it only recently activated on my computer. Download Statusbar just wasn't working the way I wanted so I decided to search for an answer and I found this one which works. But, if you have Download Statusbar activated, remove it first as it will error out on you and force you to restart your computer even if you remove it from your extensions. I can't say this is permanent as maybe your next update will undo this fix.
Note that he speaks with a heavy accent and he's saying to type chrome://flags/ to get the proper page up and then type Downloads which should bring up the correct page. Mine had a few more options than what his shows but you want to Disable Download Bubble and Download Bubble V2. Restart Google Chrome and it should now have your download bar back on the bottom and the button on top should be gone.
Remember, create a System Restore point first so if a problem happens, you can undo it.