We’ve been covering the rapid growth of free real-time chat application Kik, but the company seemed to hit a roadblock in the last month or so when it was pulled off BlackBerry phones and sued by BlackBerry-maker Research in Motion for alleged patent infringement.

Today, however, Kik chief executive Ted Livingston (a former RIM employee) told us that the application is still finding an audience on iPhones, iPods, and Android devices — it now has 3 million registered users. That’s really impressive for a service that launched less than three months ago. (I was just marveling at photo-sharing app Instagram, which launched at around the same time and reached 1 million users last month.)

VentureBeat founder Matt Marshall is a huge fan of the app. He praised the way it helps you find address book contacts who have also downloaded Kik, and that Kik gives text conversations on your phone a much more real-time feel by showing when messages are delivered and read, or even when your contact is typing out a response.

In discussing the growth, Livingston got theoretical, noting that “strong tie” social relationships (like your connections on Kik) are more important than “weak ties” (like most of your “friends” on a site like Facebook) and that text messaging dominates communication between strong ties. As evidence, he pointed to a presentation from Google’s Paul Adams (now at Facebook).

Livingston wrote:

Does this mean that there is a huge, yet to be seen social network for your strong ties that will be built on “text messaging 2.0″? A network that will be fundamentally different than Facebook, designed for intimacy and immediacy rather than exhibitionism and voyeurism? I certainly think so.

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