The 31-year-old's initial deal expired following Vale's 4-0 home victory over Plymouth last weekend, but he will now remain with the League Two promotion chasers for the second half of the campaign.
Valiants manager Micky Adams said: "Liam has signed a contract to the end of the season and we're happy with that.
"We know what he's capable of doing. He's a steady Eddie. There's nothing flashy about his game and he doesn't get many headlines, but we're pleased to get him, particularly with the injury to John McCombe."
McCombe recently suffered knee ligament damage, and Chilvers will again take his place in the squad for Saturday's top-of-the-table clash at leaders Gillingham.