Shoot, I completely overlooked that, I could have sworn I saw some people growing it in colder climes. Oh well!
How about a native honeysuckle? Any other suggestions?

Why not ask the neighbors if it would bother them. They may think the fence is as ugly as you think it is, and encourage you to spend your own dime to make it look nicer.

David

The neighbors would love to see the fence hidden, but don't want to do any real work to maintain it, and can't/won't chip in for a new fence. They know nothing about plants, so they are trusting me to pick something they'll be able to handle. I am thinking that native honeysuckle may fit the bill. Anyone see downsides to this plant?

Steelglow,
How big is the fence?
Do you think you could afford a reed or inexpensive bamboo fence to cover it up? You just wire it right onto your chain link fence, it's easy.
Check at big box stores and online for one of those fences.
I had native honeysuckle, it was beautiful coverage for 3 years, I had to move, but my neighbor, like yours with just lawn, was so sweet and allowed me to trim the vine on her side when ever I needed to. We were friends.
THe vine will grow towards the sun, and if the sun comes from your neighbors side, it will grow that way.
If you don't want your neighbor upset about the vine hanging a couple feet over onto his side, opt for the reed fence, and plant shrubs in front of it on your side.
But, if you don't mind trimming it, yes, it is a good privacy screen and will grow rather quickly for you.
Train it onto the fence, they don't twine like other vines.
Good Luck!

Even tho the neighbors won't chip in for a new fence, or help maintain the vines it seems you have plenty of freedom to do what you like with the fence. Maintain both sides yourself. Also, fence companies make slats to slide into chain link fences. These come in different colors. Remove the slats as the vines grow and cover the fence. May seem like you are putting lipstick on a pig, but vines do seem to make old fences look good.

Grow whatever you want and maintain both sides :)

I would bake some cookies, take them to the neighbor, and ask what kind of plant they think might be best. Ask for a couple of choices.

That way, if something happens with it, it is part their choice.

I had a neighbor at my previous house that got upset when I planted some morning glories on the fence. She rarely went outside, her beef was not my choice of plant, but that I didn't ask.