Speaking with RadioTimes.com, Chibnall made it clear that Broadchurch is getting his full devotion at the moment, saying that he's focusing on editing the third season before shifting his focus to the Doctor.
And because of those commitments—and his desire to give Moffat and Capaldi as much freedom as possible to finish the series as they see fit—Chibnall isn't expected to undertake his search until the middle of the year.
Chibnall will have the final say on who the Doctor is, but the report says he'll have to get confirmation from BBC executives before they can move forward.
While the production is still set to be ready for airing in 2018, Chibnall is also expected to take a vacation when his duties on Broadchurch are over. So don't expect to find out who will be the star of the next series of Doctor Who until later this year. MUCH later.
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Doctor Who returns for Season 10 in April 2017.