Council tenants have argued a plan to place surface-to-air missiles on their tower block during the Olympics could make them a terrorism target.
Residents of Fred Wigg Tower in Leytonstone, east London, have applied for permission for a judicial review at the High Court.
A judgement is expected on Tuesday.
The residents' barrister, Marc Willers, said their block could become the "focus of a terrorist attack" to make an "evil statement".
Mr Willers told Mr Justice Haddon-Cave: "It is the unprecedented siting of a military base or missile site in peace time on English soil that brings us to this court."
Of the residents, he said: "They have a fully justified fear that installation or deployment of the missile system on the roof of the Fred Wigg Tower gives rise to the additional risk that the tower itself may become the focus of a terrorist attack.
"That fear is not just genuine and legitimate but justified given the nature of the forthcoming occasion - the Olympic Games - and given the nature of the deployment and the current threat level, which is said to be substantial."
Mr Willers filed documents to the court calling for the residents to be moved out of their homes and compensated during the Olympics if the missiles are set up.