Yes, you can do that. I've done it in the past but when we sold the house I made it a point to remove all hangers from the trees. The link below has more info.

We often use the pole mount bracket to hang our heavier feeders. A little concrete in the ground stabilizes the pole and doing a top mount gets the feeder about 6' off the ground. http://www.backyardbird.com/birdhousemount.html

Here is a link that might be useful: hardware on trees

Yes,it's safe. I just closed off four tap wholes where I was gathering maple sap for sugaring. The tree will heal itself.

Two small holes won't hurt a tree that has branches 30' off the ground! Go ahead and put up your plant hanger. May I suggest that you hang the feeder away from the prevailing wind, if that is a position where you can still see it? We lose a lot of birdseed when the feeder sways in the wind, although the birds find their dinner on the ground.

Thanks everyone! I'll start looking to see where I can put it...now if I could just keep the deer away!

Actually you can kill a tree by putting holes in it, depending of course on the type of tree you have. Many evergreens dont like to have their bark destroyed at all. Yet if you have a birch it will heal up quickly. Hope you have a tree that does not mind being drilled into.

You could definitely do it, but I would worry more about the damage to the tree. If up high enough, and hanging from a branch, I can't see the birds having a problem with a wobbly feeder. I take a lot of joy watching the birds from our various feeders.

I managed to loop a chain over a high branch on one of our trees, and did a tiny anchor lower down that I can reach. I can raise and lower the feeder from that anchor.

It might be equivalent to the same thing you want to do -- but I don't feel like that anchor for the lowering-chain is much compared to supporting the whole feeder weight (the weight of the feeder is looped over the branch vs. just a tiny anchor for the chain to raise and lower the feeder). However, trees are tough. Good luck and get a great bird book. I love watching our birds and feeding them :)