How I've Waited For You... Probably the most significant chapter (so far). I'd say this was the chapter Urusei Yatsura started to change. At least explicitly.
Ataru finally realizes that Lum is pretty and falls for her for the first time...
It's also the first time Lum actually helped out Ataru (even if he didn't deserve it). It showed that she actually cared for him and didn't simply obsess over him like in previous chapters.
The way both anime handled this chapter was also really good. Especially the original which made it a Christmas special and the first full-length episode.
The circumstances might've been changed (since Mendo hadn't appeared in the anime yet) but it was still one of the best episodes of the series.
And even though the Remake version wasn't as good as the original episode 10, it still did a fantastic job adapting this chapter.