[MLD-Grounds-Keeper-Willie]

Good question. Remember the points that I made. Gollum killed Deagol because of the overwhelming desire to posses the ring and partly because the ring clouded his judgement. He was new to the ring then. I said that gollum wanted to let go of the ring even though it didn't look like it. I think that it was deep down, in the part of gollum's mind that was still gollum, that part wanted to let go. His slow rehabilitation might have helped too. Maybe, he was being cured of the ring, if even a little. He also got compassion from Frodo, and Frodo was the first person to give him a chance ever. I think that gollum really wouldn't kill him because of his healing, but maybe because he respected Frodo. Also, he felt sorry for Frodo himself. Gollum was once a ring bearer himslef, and he had it the longest besides sauron. He knew very well the struggle that Frodo was experiencing. Frodo gave gollum pity and compassion, and a chance. In return, gollum gave Frodo obedience and guidance to some degree, and sympathy and compassion.

Now that is the brighter side of the answer. Here's the darker. Maybe Gollum was waiting for a chance. I think he could have wanted to build his trust on Frodo, and then trap him. Think of Shelob.

There are other points as well, but I don't feel like saying them all. And it sucks all the fun out of these topics when you say all the points and no one else has a chance to.

To see a similar discussion, go look for the thread I showed in my 2nd to last reply.