Board Thread:Naruto Discussions/@comment-26800188-20150721182335/@comment-26369387-20150812181936

What Hexed said. Kakashi invented Chidori before he got Sharingan, but Minato saw its risk(because of tunnel effect), so he told Kakashi not to use it too much. With Sharingan, the problem was solved.

Sasuke could use Chidori right on the bat, thanks to his own Sharingan, but he also improved it so that he doesn't need to run every time he uses it.

So, Sharingan helps, but in the end you don't necessarily need it to use Chidori.