As the company of hobbits (Frodo, Sam, Merry, and Pippin) continued their expedition from Tom Bombadil's house and came to the Barrow Downs, they encountered a Barrow Wight that may have been strengthened by a recent visit of the Witch King of Angmar, Chief of the Nazgul.

From Unfinished Tales, the Hunt for the Ring (here):

The Black Captain did not know whether the Ring was still in the Shire; he had to find out. The Shire was too large for a violent onslaught...; he must use as much stealth and as little terror as he could, and yet also guard the eastern borders. Therefore he sent some of the Riders into the Shire, with orders to disperse while conversing it; and of these Khamul was to find Hobbiton where "Baggins" lived. ... But the Black Captain established a camp at Andrath, where the Greenway passed in a defile between the Barrow-Downs and the South Downs; and from there some others were sent to watch and patrol the eastern borders, while he himself visited the Barrow-downs.

Is there a timeline in Tolkien's notes to describe how closely in time the Witch King's visitation of the Barrow Downs occurs, in relation to Frodo's visit? The 'near encounters'/'close escapes' of the company of hobbits to the Nazgul is quite intriguing.