[Boromir88]

Gollum makes two promises in this chapter. By his end, he keeps one of them, the other he breaks....

"And what would you swear?" asked Frodo.

"To be very very good," said Gollum. Then crawling to Frodo's feet he grovelled before him, whispering hoarsely: a shudder ran over him, as if the words shook his very bones with fear. "Smeagol will swear never, never, to let Him have it. Never! Smeagol will save it. But he must swear on the Precious."

"Down! down!" said Frodo. "Now speak your promise!"
"We promises, yes I promise!" said Gollum. "I will serve the master of the Precious. Good master, good smeagol, gollum, gollum!"

Then Tolkien gives us this small paragraph of foreshadowing, and the events to happen, up until Gollum thinks Frodo "betrayed" him...

At once Gollum got up and began prancing about, like a whipped cur whose master has patted it. From that moment a change, which lasted for some time, came over him. He spoke with less hissing and whining, and he spoke to his companions direct, not to his precious self. He would cringe and flinch, if they stepped near him or made any sudden movement, he avoided the touch of their elven-cloaks; but he was friendly, and indeed pitifully anxious to please. He would cackle with laughter and caper, if any jest was made, or even if Frodo spoke kindly to him, and weep if Frodo rebuked him.

This is coming straight from Tolkien, not from character's dialogue, or from their conscious thinking, but from Tolkien. Gollum did "change," he wasn't putting on an act, trying to lull them into a false sense of security. He honestly changed, and I believe if Gollum had not misunderstood the Hennuth Annun situation, then he wouldn't have tried to kill Frodo. A few paragraphs earlier, Tolkien compares the Frodo and Gollum relationship as a master-dog one. Being a dog lover, and just recently getting a new puppy (5 months now, cocher spaniel) dogs are quite loyal animals. They don't hold grudges, if you yell at them for doing something they shouldn't, they will go off and whine, and you'll feel bad, but they'll wake up the next day happy and ready to start a new day. They watch over you (which we see Gollum also do later on)...and so on, the point is not to brag about dogs, but to show the comparison between a dog/owner relationship, to that of Frodo's and Gollum's. A comparison that is echoed in the paragraph above.

But in that same paragraph we also have some more foreshadowing, but a little darker than the previous passage above...

Sam said little to him of any sort. He suspected him more deeply than ever, and if possible like the new Gollum, the Smeagol, less than the old.

This mistrust could be something that hurts Gollum, more so than being "tricked" by his master as he thinks it, something we'll have to look at when the time comes.

Edit:

Something davem has been talking about recently, is mercy, and the absence of mercy. This again is seen within this chapter, which is filled with pity. Gollum does deserve to die, and is surely not worthy of Frodo's mercy. Despite this Frodo still shows his pity, and offers it to Gollum. Gollum reacts to it in a positive way, and we see hope that he could change. Opposite of Sam, who suspects Gollum, and keeps a closer eye on him, distrusting him, showing him no mercy. Again makes you wonder, if Sam would have shown mercy to Gollum, like Frodo, what would have happened? (Don't worry Sam, I still love ya).