This is now possible in Chrome 57. Just visit DuckDuckGo, perform a search (search for anything), then visit Settings > Search engine and DuckDuckGo should be listed at the bottom of the page.
After doing the DuckDuckGo search, if you still don't find DDG on Chrome's Search Engine page, you may (as I did, using Chrome 61) have to go to DuckDuckGo.com and then do the following:
- Tap DDG's three-line symbol (≡) in the upper-right corner of the webpage.
- Tap Other Settings.
- Scroll down to the Install DuckDuckGo section, and make sure "Show links to instructions . . ." is set to On.
- Tap Save and Exit.
- Back on DuckDuckGo.com, tap the Add to Chrome button if you see it; if you don't see it, scroll down to find the Add DuckDuckGo to Chrome button, and tap that.
- A "Take Back Your Privacy!" message should pop up. Follow its instructions:
- ) Tap the Google app's three-dot symbol () in the upper-right corner of the browser window.
- ) Tap Settings, then tap Search engine.
- ) Now, DuckDuckGo should be there at the bottom for you to select; at least, it was for me.
I hope this works for you too!