But: "Basecamp Personal is offered exclusively to existing Basecamp users (or anyone with a 37signals ID). You don't have to be the owner of a Basecamp account - you only have to be a user on a Basecamp account. We plan to open Basecamp Personal up to the wider public in a few months."
http://basecamp.com/pricing: "Pricing Starts at $1/day", so, no.
Search, hit: https://basecamp.com/personal "... $25 per project. Pay once, no recurring fees."
But: "Basecamp Personal is offered exclusively to existing Basecamp users (or anyone with a 37signals ID). You don't have to be the owner of a Basecamp account - you only have to be a user on a Basecamp account. We plan to open Basecamp Personal up to the wider public in a few months."