In the top right of your browser, you'll find the profile icon. Click on it, and a dropdown will appear. Then click Manage People.
In my case, I'm deleting a profile called "Person 1". If you hover over the profile square, the details icon will appear. Click it.
A dropdown will appear with a few options, click Remove This Person. You'll be given an opportunity to confirm your intentions, and you'll need to click Remove This Person once more.
At this point, you've delete the Google Chrome profile!