The competition begins today and will run for ten days across the @CapitalOfficial and @ThreeUK Instagram accounts.
The presenters will be based in Los Angeles from Monday 1 February in the week-long run-up to the Grammy Awards, An Instagram video will show an open suitcase stuffed with prizes, such as iPads, Sony Xperia phones, Beats headphones and Ray-Bans.
To win, Capital listeners must screengrab their chosen prize and re-post the image using the competition hashtag #grabtowin.
The scheme has been planned and created by Mindshare Partnerships, to promote Three’s 'Feel at Home' campaign, which allows customers to use their phones abroad cheaply.
Wieden & Kennedy London's TV ads broke last week, with a spot featuring three Welsh surfers going on and on about their holiday, and a warning that a social media barrage would come from Three customers on holiday.
Mike Gordon, the chief commercial officer at Global, said: "This campaign gives Three access to Capital's highly engaged audience on-air, online, and on social media. The use of Instagram in the #grabtowin competition is the first of its kind.
"It’s a great example of how social media can be used in an innovative and targeted way as part of a bigger campaign."
The campaign will also tie to some high-profile interviews in LA, including Taylor Swift, Cameron Diaz and Usher.
Pippa Whybourne, the lead communications manager at Three UK, said: 'The online presence and aspects such as the Instagram competition have been hugely successful to date and demonstrate great ways of connecting with the show's listeners in innovative, creative and engaging ways."