Chilaka, 32, spent last season at Hyde United and has previously played in National League North for Bradford PA, Harrogate and Gainsborough.
Manager Paul Rawden said: “Chib gives us another option upfront, we've got plenty of matches coming up and we felt we needed someone else in.”
It took just 19 minutes on his debut for Chilaka to open his account for the Gingerbreads, who conceded two late goals in heartbreaking fashion to draw 2-2 at league leaders Matlock Town on Tuesday night.
He is cup tied for their FA Cup clash at Nantwich on Saturday.
Keep up-to-date with our exclusive email newsletters.
Subscribe