It's been a good nine months since the Sprint Galaxy Nexus received its last OTA to Android 4.2.1, and now the jump to 4.3 is beginning its rollout. In a bit of awkward timing with the expected launch of Android 4.4 for other Nexus devices, Sprint has just posted on its community site that the update is rolling out now.
As is usually the case you'll have to wait somewhere in the range of two weeks to get the software update as the rollouts happen both gradually and at random. The latest software version is now "GJ04" if you want to make sure you're on the latest build — keep an eye on your phone for that update.
Source: Sprint; Thanks, d14racer24!