SHJ,
First Reserve took the company private in 2008 then re-listed 26% of the shares on the NYSE last Jan. They retained 74% themselves though.
CD&R came along in the middle of last year and bought FR's 74%.
26% of the company remains publicly traded though. These numbers do fluctuate though so if you go to the SEC filings page I linked above, you'll see the ownership structure.
FR still own most of the the debt (off balance sheet) which they issued to buy CHC in the first place (like the Glazers at Man Utd if you're a football fan) but own no equity (shares) in the firm now.
It's typical Private Equity.
NWS