SUBSTITUTE Iain Howard capped a comfortable victory for the Blues with an 86th minute goal against their Yorkshire hosts.
Luke Holden broke the deadlock in the 14th minute when he slammed home a low 12 yard shot from Matty McNeil's pass on the edge of the area.
Matty McGinn doubled Chester's advantage in the 27th minute when he netted his ninth goal of the season and his sixth from the penalty spot after Chris Simm fell to the ground under a challenge from Alex White.
McGinn made it 3-0 in the 36th minute after weaving his way beyond two defenders and rifling a low 15 yard shot into the bottom right corner of the net.
Jerome Wright carved out Chester's fourth goal after racing 50 yards down the left wing before finding Iain Howard who turned the ball home from close range.
WHITBY TOWN (4-4-2): Campbell; Lyth, Robinson, White, Burgess; Hawkins (Williams 69), Martin, McTiernan, Smith; Tymon (Faichney 55), Leeson. Subs (not used): Blackford, Hassan, Courtney.
CHESTER (4-4-2): Danby; Brownhill, Horan, Taylor, McGinn; Booth, Brown (Wright 77), Powell, Holden (Howard 53); McNeil, Simm (Ellison 62). Subs (not used): Smith, Baynes.
REFEREE: Matthew Diciccho (Middlesbrough).
ATTENDANCE: 652.