Steve McClaren's Twente lead the standings with 40 points from 18 matches but can be overtaken by PSV Eindhoven, who have a vastly superior goal difference, if they beat NAC Breda on Saturday.
Alkmaar dominated the first half and were close to scoring when a fierce volley from Adam Maher was headed off the line by Douglas.
Chadli struck for Twente two minutes into the second half when his shot, slightly deflected by an Alkmaar defender, went past keeper Esteban Alvarado.
U.S. international Jozy Altidore nearly levelled for Alkmaar before Dusan Tadic set up Luc Castaignos to double the lead 15 minutes from time and Chadli settled the match with an outstanding lob from 16 metres.
"My first goal went in with a bit of luck but it helped us into the match," Chadli told Eredivisie Live TV.
"I'm still not at my best and improving as I just came back from injury."
Ajax Amsterdam, who on Sunday visit their nemesis Utrecht who have won their last three home matches against the champions, are third with 36 points, one ahead of Vitesse Arnhem who visit Heerenveen.