But Forest Green are still seeking their first goal and point from the new campaign as Gary Owers' men slid to a third successive loss.
Chillingworth struck in the 20th minute when he was left totally unmarked some 18 yards from goal, allowing him to bury a thumping header from Paul Watson's left-wing cross, giving Steve Williams no chance in the visitors' goal.
Watson had already curled a free-kick straight at Williams and it was the home side who called the shots in the first half, with Rovers only making an impression late on when Mark Beesley volleyed over the crossbar and then cut inside to force a save of sorts from Nicky Eyre in the home goal.
Veteran midfielder Dave Savage earned plaudits for a tireless display in the heart of the home midfield and he was at the centre of most of their best moves, although Diamonds' best other first-half chance came after a one-two between Chillingworth and Jackson which ended with the latter having a shot blocked by Keith Nicholson.
If Diamonds dominated the first half, the visitors had clearly been roused by Owers during their half-time break and they produced easily their best moment of the match two minutes after the restart.
A long throughball by the tireless Alex Meechan sent Charlie Griffin scampering clear down the right, and the striker connected with a sweet first-time volley which flashed past the far post.
Diamonds responded with right-back Glen Wilson finding Savage, who cut inside before firing a shot across the face of the visitors' goal and wide.
Minutes later Chillingworth almost sniffed out a second but his spectacular volley from the edge of the box after another Savage cross was well saved by Williams.
Beesley should have levelled in the 65th minute but blazed over the bar with only the goalkeeper to beat.
It was to prove an expensive miss, as Diamonds doubled their lead ten minutes later.
The move stemmed from a right-wing cross by Michael Rankine and when Marcus Kelly nodded the ball back into Jackson's path, the striker's shot took a deflection off Mark Preece and looped over goalkeeper Williams and into the net.
If Williams felt hard done by, he at least had the satisfaction of keeping the score down in stoppage-time when he raced from his goal to deny substitute Lee Tomlin, who was rapidly bearing down on him.