* U.S. offshore driller lists in Zurich at 95.20 Sfr

* Shares rise to 96.30 Sfr shortly after open * Could join blue-chip SMI in June

* Insurer Swiss Life candidate for SMI removal (Adds details)

ZURICH, April 20 (Reuters) - Offshore driller Transocean Ltd RIG.NRIGN.S debuted at 95.20 Swiss francs ($89.39) on the SIX Swiss Exchange on Tuesday, adding to its New York listing and paving the way for a place in the SMI Swiss blue-chip index.

The listing of Transocean, which moved its domicile to Switzerland from the Cayman Islands for tax reasons in December 2008 and has a total market capitalisation of around $28 billion, is the Alpine nation's biggest since the merger of Swiss Bank Corporation and Union Bank of Switzerland to form UBS UBSN.VXUBS.N in 1997.

Transocean, the world's largest offshore drilling contractor, could barge its way into the SMI .SSMI as early as June 21 if it meets certain conditions, even though the index is usually only reshuffled once a year, in September.

“We believe the listing of Transocean’s shares on SIX is an excellent way to increase interest in Transocean among Swiss and European investors and reaffirm our presence as a Swiss company,” said Transocean President and Chief Executive Steven Newman.

Shares in Transocean traded at a high of 96.30 Swiss francs ($90.42) at 0710 GMT in a firmer Swiss market after opening at 95.20 francs. The stock gained 1.3 percent in New York on Monday to close at $88.29.

The owner of a fleet of 140 drilling rigs will likely muscle insurer Swiss Life SLHN.VX, with a market capitalisation of 3.8 billion Swiss francs ($3.61 billion), out of the SMI.

This would making Swiss Life the second insurer to be knocked out of the SMI in under a year after Baloise BALN.VX lost its place in the blue-chip index in September 2009.

The alternative candidate for being pushed out of the SMI by Transocean is Swiss drugs industry supplier Lonza LONN.VX.

Transocean, which reported operating revenue of $11.6 billion and $3.7 billion in net profit in 2009, has said its shares will be included in the all-share Swiss Performance Index .SSHI on the second day of Swiss trading.

Transocean was followed to Switzerland in 2009 by others in the energy sector, including rival Noble Corp NE.N, which had also been based in the Caymans, along with oilfield services company Weatherford Ltd WFT.N and engineering company Foster Wheeler Ltd FWLT.O, both formerly domiciled in Bermuda.

Apart from a stable tax regime, the companies also cited the need to be closer to customers and the growing number of Eastern Hemisphere energy projects as reasons to abandon their island paradises for landlocked Switzerland. (Reporting by Jason Rhodes; Editing by Louise Heavens) ($1=1.065 Swiss Franc)