How would I create a text box that guesses what you are trying to type in as you are trying to type it?

We are currently developing web-based software using PHP and a MySQL database.  We are looking to create a text box that guesses what the user is trying to type in as each consecutive letter is typed.  The actual list that the text box has to guess from is not that big (less than 100).  Also, the guesses would ideally appear below the text box as the letters are typed.

We are worried this will bog down the system's resources, especially with many users.  How do you recommend we handle this?  Is there an application that we can download/copy/paste to handle this?