Police were called to a disturbance at a property on Henderson Drive at approximately 6.50am on Saturday, August 17.
Officers and paramedics from the South East Coast Ambulance Service went to the scene.
Upon arrival, they found a woman with injuries consistent with a stabbing.
She was pronounced dead at the scene.
The suspect, a man in his 20s who is believed to have been known to the victim, was taken into custody shortly after the incident.
Ernestas Juska, 20, of Henderson Drive, has been charged with her murder.
He also faces charges of committing a sexual offence against the deceased woman.
Juska is currently in custody and is scheduled to appear in Medway Magistrates’ Court on Monday, August 19.
