Thank you everyone!
Yes, the border is done in chain stitch. Well, technically reverse chain stitch. I found this simple tutorial from Jenny at Sublime Stitching http://sublimestitching.com/pages/how-to-chain-stitch
though she calls it Simple Chain Stitch. The result is the same as regular chain stitch, and I love how it really played into the intertwined Celtic vine look I was going for.
And honestly it didn't take me very long. Maybe an hour or two per color. The best thing I did prepwise, was to color in each strip with a correlating colored pencil, so when it was time to stitch, I just followed the same color as the thread. Otherwise, (knowing me) I would've ended up ripping out sections repeatedly.