I'm pretty sure that's a Railroad Vine , Ipomoea pes-caprae.
It's also called a Beach Morning Glory.

I wondered the same, but the seed leaves (third picture) seemed wrong. Most Morning Glories have sort of ear-shaped seed leaves, but this one had spade-shaped seed leaves. Still, it does bear a striking resemblence, perhaps it is just some mutated variety with different seed leaves. I hope it survives Tuesday's frost/freeze. Maybe I'll cover it with a nursery pot to ensure it does.

What about beach bean (Canavalia rosea/maritima)?

Beach Bean does look like a possibility. I was about to dismiss it asmost pics show a longer, smoother vine, but some pics do show a similar segmented growth habit. Either way, it looks like one for me to watch as it grows.

I've been watching to see if anyone knew for sure. I agree, wait and leave it alone to see if it flowers or fruits. It kind of looks like the Milk Pea photos I've seen but then some of the photos have more elongated leaves than that. I have some growing wild here but it's hard to tell how large those leaves are and the ones here the leaves aren't that big. Here's a webpage and photo.

Here is a link that might be useful: {{gwi:980542}}

Well, I have been thinking on it, and I do recall plucking a 'pea pod' that was dangling from a vine growing through a Seagrape at Playalinda Beach. I tried to germinate the seeds in that pod, but none took and I ended up tossing them all my compost (I've tossed a lot of failed seeds in my compost pile!). I want to say that was back in the tail end of the Summer of '13, so if this is one of those seeds, it took its sweet time germinating.