Emily needs to be at relationship 4 to finish chapter 1.
Provided you've given her at least 2 compliments already, chosing the "take a nap" option in the afternoon should get you the relationship 3 scene (it can be that you'll get the afternoon dream first, in that case you need to choose "Take a nap" on the next afternoon again).
After that, if you've given her a 3rd compliment, you should only need to choose the "Talk with Emily" option on her door in the evening to get her relationship 4 scene.
What's really important is that you need to have downloaded or updated to version 1.09b or c, because the original 1.09 unfortunately still had a bug that prevented reaching relationship 4 with Emily.