I agree with Daylesewblessed......."hope"..........."Cedar" chest, from the open picture it looks like it is cedar lined. I have Not seen a cedar chest that had a covered top like that one but the top may be damaged is why they covered it with fabric. If indeed it is a ceder lined chest you may not want to store fabric in it as the cedar will give the fabric an odor (the cedar odor will wash out).
Do Love the fabric you chose to put on top.