The former West Indies Test batsman, aged 42 and 240 days, hit two sixes and 21 fours in his eight-hour innings.
Overnight partner Jordan Clark departed for 140 after their stand reached 243.
Paceman Mark Footitt claimed 5-118 for the home side, who lost Scott Borthwick to the final ball of the day to close on 112-2, 358 behind.
Resuming on 294-6, Chanderpaul and Clark stayed together for another 24 overs before the latter was adjudged to have edged to Rory Burns at slip as he tried to sweep spinner Gareth Batty.
But they had already set a new Lancashire seventh-wicket partnership record against Surrey, beating the 198 by Alexander Eccles and John I’Anson at Old Trafford in 1902.
Left-hander Chanderpaul had earlier tucked Footitt away for two runs to reach three figures and he continued batting serenely through the afternoon session, despite needing a runner because of a thigh injury.
Footitt removed Stephen Parry and Kyle Jarvis in the space of three balls, with the help of wicketkeeper Ben Foakes, and Chanderpaul was finally removed when he was caught at extra cover off Batty.
After winning their opening game against Warwickshire, Surrey also made the most of a good strip at the start of their reply, with Stoneman and Burns adding 67.
Stoneman then fell lbw to Clark for 40, and although Burns survived to stumps on 48, Borthwick’s exit – caught behind off Jarvis for 19 – was a disappointing ending for Surrey.