Lyric discussion by Lanta 

As a couple of other people have said, this song was written about pop singer Natalie Imbruglia who clearly has deep green eyes.

Chris Martin dated Natalie briefly, before she got back together with (and eventually married) Daniel Johns of Australian band Silverchair, who she'd been going out with prior to Chris. That's why Coldplay stopped playing it in concert.

@Lanta Natalie Imbruglia's eyes are blue...

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