Chanderpaul, who has batted for more than 15 hours this series, was 44 not out with Dwayne Bravo 43 not out, adding an unbeaten 77-run stand after they had come together when the West Indies collapsed to 55 for 4.
However both batsmen were given lives with Chanderpaul dropped on nine and Bravo surviving a tough chance on 25.
England were in charge early with Sidebottom striking after rain had washed out Friday's first day and delayed Saturday's start by three hours, after captain Michael Vaughan won the toss and elected to field under overcast, seam-bowler friendly skies.
West Indies stand-in captain Daren Ganga was out to the first ball of the Test as he turned Sidebottom straight to Alastair Cook at short leg for his second duck in as many innings.
Fellow opener Chris Gayle decided that attack was the best form of defence as he proceeded to smash 28 from 24 balls including three fours and a six, before the recalled Matthew Hoggard had him trapped LBW in the eighth over.
The next over, 32 for 2 became 34 for 3 when Devon Smith, deliberately playing no shot, was bowled by a Sidebottom ball that hit his off-stump.
Sidebottom was in the thick of the action and took a catch at mid-off to help dismiss Runako Morton who drove at a Stephen Harmison delivery off the last ball of his second over to be out for six.
Harmison, on his Durham home ground, might have had an even better return when Bravo, who had taken 20 balls to get off the mark, saw a low drive brush the bowler's fingertips after tea.
Meanwhile Chanderpaul, who has an impressive average of nearly 46 in 104 matches at this level, reached the milestone of 7,000 Test runs with a leg-glanced four off Harmison, but was then dropped when he edged a drive off Hoggard to Ian Bell at third slip who shelled the head-high chance.
At stumps Sidebottom had impressive figures of 2 for 34 from 11 overs, and was well supported by Hoggard (1 for 35 off 15) and Harmison (1 for 46 from 10.4).
The Windies made two changes to their team from the third Test, with all-rounder Marlon Samuels replacing the unlucky Darren Sammy who took 7 for 66 on his Test debut at Old Trafford but subsequently strained a hamstring while batting.
Fast bowler Daren Powell, dropped in Manchester, replaced fellow quick Jerome Taylor.