An ancient Vulcan technique of killing by snapping the neck, once regarded as a merciful form of execution, used to murder the Tellarite ambassador Gav aboard the Enterprise.
Tal-shaya is a precise way of breaking the neck that causes immediate death. Spock describes it as having been considered a merciful form of execution on Vulcan in ancient times.
It figures in Journey to Babel. While the Enterprise carries delegates to the Babel conference on the admission of Coridan, the Tellarite ambassador Gav is found dead, killed by tal-shaya. Suspicion falls on Sarek, who had quarrelled with Gav in public and who has no alibi because he was hiding the effects of a heart condition.
The real killer is Thelev, an Orion agent surgically altered to pass as an Andorian aide, whose aim is to sow distrust among the delegates and keep Coridan's dilithium open to raiders. The episode is the only one in which the technique is named.