Thats a pretty colorful piece there, I can understand why you'd think it was painted because I would. The only real difference between jasper and chert are the size of the micro-crystalline structure. There are also differences in the iron and manganese content as well. What sets them apart for me is the luster of the material and the color. Cherts have a larger crystalline structure and not much color, usually just banding, so the luster is flat in most cases. Jasper's tend to show strong color's and the luster is glassy to waxy due to the smaller crystalline structure.
I call what you have there a Jasper.