Need help identifying this instrument please
 

Looks like I'm not allowed to link to the YouTube video, but it's "I Don't Know How to Love Him" from Jesus Christ Superstar, the video is the first result and is 5:03 in length.

I'm trying to identify the sweet sounding instrument that you can hear at 1:05, then later at 2:40 and 4:00+. It sounds like a piccolo, but I'm not sure.

I've wanted to know for ages but only just thought to ask! Any help would be hugely appreciated - I want to buy whatever it is and learn how to make that sound.

Thanks!