Chanderpaul, batting at No 3, made 116 not out in a total of 278 for five after West Indies lost the toss.
He'd moved up from No 5 after top-scoring for the West Indies with 53 not out during their 79-run defeat in Sunday's series opener at Lord's.
Together with Marlon Samuels, dropped on 14 by Paul Collingwood, the England captain, off his own bowling on his way to 77, he put on 175 for the third wicket in 34 overs.
This was Chanderpaul's seventh hundred in 219th one-day international as West Indies looked to level the three-match series at 1-1.
The 32-year-old had been a thorn in England's side during the hosts 3-0 Test series success, averaging 148.66, and this was another example of his ability to pace an innings after he took 10 balls to get off the mark.
In all Chanderpaul faced 122 balls with three sixes and 10 fours.
The third-wicket duo came together when Chanderpaul was on one, their side 67 for two in the 13th over.
West Indies captain Chris Gayle got the innings off to a brisk start with some powerful sixes, the best a straight hit over the pavilion sightscreen off first change Stuart Broad.
Such was the damage, the ball was replaced with West Indies on 48 in the eighth over.
James Anderson ended the first-wicket stand two runs later when Devon Smith, on 17, edged a cut to wicket-keeper Matt Prior.
Gayl, having lofted Ryan Sidebottom, in for Liam Plunkett, over long-off for six was out next ball when a delivery that 'stopped' saw him chip a simple catch to Anderson at mid-on.
The run-rate slowed, the second fifty up in 16 overs but West Indies were keeping wickets in hand, aided by Collingwood's miss.
Chanderpaul, upping the tempo, lofted Collingwood over long-on for four and six off successive deliveries in the bowler's next over as he took advantage of the shortened boundaries.
England gave Michael Yardy, in for frontline left-arm spinner Monty Panesar, just six overs during which he conceded 29 runs.
Medium-pacer Dimitri Mascarenhas was England's most economical bowler with none for 31 in 10 overs.
But England's quicks suffered as West Indies scored 102 in the last 10 overs.
After a brief rain break, Chanderpaul, on 43, cut Mascarenhas to backward point where Ian Bell couldn't hold a tough, one-handed, diving chance.
Chanderpaul completed his fifty in 85 balls with one six and four fours, Samuels reaching the landmark in one ball fewer with the same boundary count after he'd struck Mascarenhas for six over long-on.
Samuels's innings eventaully ended when he steered Broad to Sidebottom at short third man, West Indies 242 foe three.
The series concludes at Trent Bridge on Saturday.
West Indies 278 for 5 (Chanderpaul 116*, Samuels 77, Gayle 36; Stuart Broad 2 for 49, Sidebottom 2 for 56) Vs England. (yet to bat).