Further to what Siegel Clyne says, the next episode, "Nameless," will be streamed beginning 1 May, on
Yahoo Japan. Episode 5 will come out in July and ep6 in September.
NicoNico Douga has also established a page for the show on the
Niconico Anime Channel. I'm not certain, but I believe you can watch the anime channel even if you aren't registered on NicoNico.
The Eve no Jikan
official site says they had an all-night showing of the three episodes of Eve no Jikan at
Theatre Shinjuku, with Nojima Kenji as the guest.
It also says that the DVD of ep3 went on sale April 1, and that if you buy the limited edition (Y1300) through the website you get newly-made trading cards of Sammi, Rina, and Kouji.
With info from
Ota-Suke.
The comparison to Chobits, while apt in many ways, is also quite misleading. I can't think of many anime that are more different from each other than these two, in style and in substance.