It happened around 11:15 Sunday morning on the 800 block of Adams Street.
After receiving a 911 call, officers arrived to find a 68-year-old man with stab wounds to his chin, chest, face and abdomen.
An investigation revealed that the victim had a dispute with his neighbor, 68-year-old Robert Lee Jones, on Saturday evening.
The following morning, when the victim was out hanging clothes in his backyard, police say Jones attacked him with a sharp object.
The victim was taken to Christiana Hospital in serious but stable condition.
Police located and arrested Jones who now faces charges.