Cooper, who was a regular in the Tigers' team towards the end of last season but has yet to play for the first team this campaign, could make his Spireites debut against Hartlepool at the Proact Stadium in the FA Cup first round on Saturday.
The 21-year-old becomes manager Paul Cook's first signing since he took charge last week.
Cook said: "We are delighted with the signing of Liam Cooper.
"He is a player that attracts a lot of interest from clubs, and not just in this division.
"Liam brings great experience, he has played in the Championship, and with Sam Hird suspended and Neal Trotman injured it was important that we got someone in immediately, and to get a player of Liam's quality is fantastic."