The move comes only two days after another non-US citizen, Mexican-born Jose Medellin, was executed late on Tuesday night for his role in the gang-rape and murder of two teenage girls, also in Texas, in 1993.
'Violating international law'
Chi's lawyers said he should have been told that he could get legal assistance from the Honduran consulate when he was arrested in California and extradited to Texas to face charges of killing his former boss at a men's clothing store.
The failure to do so, they say, was a violation of international law.
However Chi, unlike Medellin, was not among around 50 death row inmates across the US, all Mexican-born, whom the International Court of Justice (ICJ) ruled should get new hearings in US courts to determine whether the 1963 Vienna Convention treaty was violated during their arrests.
George Bush, the US president, has called for the cases affected by the ruling to be reviewed, but the US Supreme Court ruled earlier this year that neither the president nor the ICJ could force the Texan state government's hand.
Sixth this year
The state had argued that upon his arrest, Chi had not immediately identified himself to police as a foreign national.
A judge in Texas had already refused a request from Chi's lawyer to withdraw his execution date until legislation formalising procedures for reviews of death sentence cases involving foreign nationals becomes law.
|The Supreme Court rejected Chi's final appeal [GALLO/GETTY]
An appeal seeking to halt Chi's execution - the sixth this year in Texas - was also turned down Thursday by Texas' highest criminal court.
Chi, 29, was spared the death chamber last September when the Texas Court
of Criminal Appeals stopped his scheduled punishment after the Supreme Court
agreed to consider whether lethal injection procedures were unconstitutionally cruel.
His date was reset for Thursday when the court earlier this year upheld the method as proper.