Audacity is a free and open source audio editor for Windows, Mac and Linux. It’s a great, simple editor for single audio tracks. Although it isn’t available for Chromebook, there are some neat alternatives.
TwistedWave supports Google Drive, and even looks visually similar to Audacity. However, it’s limited to editing 30 second long clips without an account – you can log in (currently free) to edit clips up to 20 minutes long.
Den Hoopingarner’s MP3 Recorder
Den Hoopingarner’s portfolio contains an excellent option from Chromebook users – a flash widget that records audio, offers trimming, and encodes it to MP3 for download. Very simple and useful. Thank you to a kind commenter for pointing this out!
HTML 5 Audio Tool
The HTML 5 Audio Editor from Plucked is an online audio editor derived from parts of Audacity. Since your Chromebook runs the Web Audio API in Chrome, this editor works great – just drag and drop audio and process with some simple effects like normalisation or linear fades.