We don't have captions built in on StreamYard, but Facebook, Youtube, and LinkedIn will add captions to your live stream for you. In addition, you can pay to add captions after your live streams with a software like Rev.com.
Google Chrome also has a built-in live captioning feature, to show captions locally inside StreamYard.
To see how to enable that, click here.
Here's how to turn on/off the captions on Facebook.
Here's how to turn on/off the captions on Youtube.
Here's how to turn on/off the captions on LinkedIn.