Chadwick's first half brace - and a third three minutes after the break - accounted for Farsley Celtic at the Jakemans Community Stadium.
Jake Wright added the icing to United's cake with a clinching fourth goal after Chadwick's free-kick had rattled Max Dearnley's crossbar.
Wright had been recalled to the United starting XI ahead of kick-off, with Birmingham City loanee Finley Thorndike dropping to the bench.
Wright had a key role in United's opener in the ninth minute - playing an exquisite throughball into the path of CHADWICK who ran on and buried a beauty past Dearnley from 20 yards.
Cameron Gregory got himself behind a Carlton Ubaezuonu effort, while Ben Pollock blocked brilliantly to deny Lewis Turner, and United were soon two goals to the good when CHADWICK robbed Turner, drew the advancing Dearnley and rolled the ball into an empty net.
It was game, set and match three minutes after half-time when CHADWICK interchanged with Ethan Sephton down the left before bending a low effort beyond Dearnley's dive to complete his first career hat-trick.
Chadwick was desperately unlucky not to score his fourth when his 20-yard free-kick smashed Dearnley's crossbar - only for WRIGHT to roll home the rebound to seal a brilliant afternoon for Ian Culverhouse's side.
Boston (4-1-2-1-2): Cameron Gregory; Tom Nixon, Luke Shiels, Ben Pollock, Ethan Sephton (Will Atkinson 77); Tom Platt (Lirak Hasani 69); Zak Mills, Sam McLintock; Billy Chadwick (Finley Thorndike 72); Jordan Burrow, Jake Wright. Subs (not used): Tre Mitford, Jo Cummings.
Farsley (3-5-2): Max Dearnley; Adam Clayton (Chris Atkinson 46, Harry Jessop 69), Andy Butler, Tom Allan; Lewis Turner, Kian Scales, Danny Devine, Carlton Ubaezuonu, Lewis Butroid; Frank Mulhern (Sam Muggleton 84), Theo Williams. Sub (not used): Tom Morgan (gk).
Referee: Dale Wootton.
Attendance: 1,981 (61 visitors).
PIC: Tim Hoff.