Preston enjoyed the better of the first half, with Lewis Neal twice denied by keeper Nick Colgan from close range.
And the visitors secured a narrow win on 55 minutes when Chilvers headed home Paul McKenna's corner.
The Tykes were not without chances, Paul Hayes and Daniel Nardiello hit the woodwork, but North End held on.
Preston boss Paul Simpson on new signing Michael Ricketts:
"He looks good and if we can keep him right and he keeps himself in good shape , he could turn out to be the biggest snip of the January window.
"It was a deserved win and we probably could have made it comfortable for ourselves with the chances we created, particularly in the first half.
"We had to dig in in the second half but we deserved it over 90 minutes."
Barnsley: Colgan, Hassell, Paul Reid, Atkinson, Eckersley, Mattis, Togwell (McCann 73), Howard, Kyel Reid, Hayes (Coulson 65), Nardiello.
Subs Not Used: Lucas, Heckingbottom, Kay.
Booked: Hassell, Nardiello, Howard.
Preston: Nash, Alexander, Chilvers, Wilson, Hill, Sedgwick, McKenna, Davidson (Dichio 90), Lewis Neal, Nugent (Whaley 84), Ormerod (Ricketts 73).
Subs Not Used: Lonergan, Jarrett.
Goals: Chilvers 55.
Ref: P Joslin (Nottinghamshire).