The private hearing is expected to continue through Monday with no comments from any of the participants, both Landis and the US Anti-Doping Agency (USADA) having agreed to the closed-door session unlike last May's open US hearing.
Landis, 32, has denied wrongdoing and fought his positive test for steroid testosterone on July 20, 2006, but a USADA arbitration panel ruled 2-1 against him last September, resulting in a two-year ban through January 29, 2009.
The International Cycling Union stripped Landis of his 2006 crown after that verdict, awarding the title to Spain's Oscar Pereiro.
In a Manhattan law office, Landis will make much the same case as he did last year, attacking the credibility of the French laboratory which handled his doping samples, and hope the global panel sees matters differently.
The CAS appeal board includes David Williams of New Zealand, Paris attorney Jan Paulsson and New York lawyer David Rivkin.
Swiss-based CAS will announce its binding ruling from Lausanne after completion of the hearing and consideration of the evidence presented.
Landis tested positive for synthetic testosterone after the penultimate 17th stage of the 2006 race. He fell back in stage 16 but rallied in stage 17 to reclaim almost eight minutes on his way to a now-disgraced victory moment.
The USADA arbitration panel noted several areas in which the French lab's handling of the test sample was improper but said the carbon ratio isotope test that showed Landis testing positive outweighed those issues.