Charlie's parents, Christopher Gard and Connie Yates, have raised more than $2 million in online donations for their son and want to try an experimental treatment, which is being offered by doctors here in the United States and at the Vatican.
Who has the right to decide if a patient, young or old, gets further medical treatment, no matter how unlikely the success?
His parents, Chris Gard and Connie Yates were in opposition, and campaigned to keep him alive on life-support, until they could travel to the United States where an experimental treatment is available.
The 11-month-old has mitochondrial depletion syndrome, an extremely rare degenerative condition which saps energy from his organs and muscles.
"There is not a person alive who would not want to save Charlie", Mr. Justice Francis said, in agreeing to a new hearing, reports The Sun. Doctors there believe Gard's brain damage is "severe and irreversible" and have said the baby may be suffering, in contradiction to the parents' views.
Charlie's parents, from Bedfont, west London, spoke out on Sunday, saying they wanted to respond to what they described as "myths" in their son's case and criticised "misinformation".
The New York-Presbyterian Hospital in Manhattan has reportedly said it would "admit and evaluate" Charlie for treatment, as long as the baby can be transported safely to the facility, Fox News reported.
Nucleoside bypass therapy is administered via oral medication and has saved the lives of two children who suffer from a similar form of the mitochondrial disease that Gard is fighting.
"There's 18 children now on the medication, they all have mitochondrial syndrome as well as Charlie".
Judge Nicholas Francis gave the couple until Wednesday afternoon to present the evidence and set a new hearing for Thursday.
On Monday, the judge instructed Charlie's parents to cite the source of all evidence, when it was produced and what difference will it make for their son. He's not, now he's still fighting so we're still fighting. It has been "amazing", said Chris Gard and it's what has been "keeping them going".
Great Ormond Street insists its view that Charlie's life-support should be switched off "is not an issue about money or resources, but absolutely about what is right for Charlie".
We don't see what's dignified about him dying - we think it's dignified that he has a chance at life and if it doesn't work then we'll let him go.
Great Ormond Street is convinced that the therapy "would be of no effect but may well cause pain, suffering and distress to Charlie".