The club says the London Legacy Development Corporation was wrong to award sole tenancy of the stadium to West Ham, and bosses want the High Court to intervene.
Lawyers representing Leyton Orient asked the High Court to give the club the go-ahead to seek a judicial review of the corporation's decision.
They began outlining arguments to a judge at a hearing in London expected to last several hours.
Lawyers representing the corporation and West Ham are expected to give their views.
- Leyton Orient