Does Chip need an Offensive Coordinator?   

  No, not Pat Shurmur, a 
real one. 
Was debating this with my brother during the week, he's still all in on Kelly and I'm not so much.  The way this team is built, it's going to live and die based on how the offense performs.  Obviously the other 2 phases are important, but given how the player $$ is spent and the style they play, they aren't going to win a lot of games 13-9.  If the offense can't consistently put up 25+  ppg then we're going to have limited success.
In looking at per drive and per play metrics over the last 3 years, the performance of that unit, Kelly's specialty, has been steadily declining, rather than improving or even maintaining at a consistent level.  Right now they're among the worst units (bottom 10) in the league in terms of drops, giveaways, yards per play, yards per pass attempt.  They're no more than middling in a bunch of other areas like points/game, TDs/game, points/drive etc.
The offense sucks and it's been trending in the wrong direction for two years.
There are positives, Ryan Mathews has been a nice surprise, Bradford seems to be slowly settling in, my biggest reservation with him is that even when he plays well, there is always a "but".  Like, he really hung tough in the pocket yesterday, took some shots and made some great throws (back shoulder to Celek was about as perfect a throw as you'll see) but, his 2 turnovers in 3 drives (along with Mathews fumble) are what took the team out of contention.
I think it's time for the offensive philosophy to take the next step though.  I think the "All Kelly" version has run it's course, and the playbook needs some input from somebody who can diversify and extend it.  It's not new anymore and while the tempo and core run plays still work at times, defenses mostly seem to have adjusted.
There's still a lot of personnel stuff to address (say it with me: Offensive Line) and I think some of Kelly's moves there have been outright mistakes (Hey DeMarco) but I still believe in his overall approach to constructing and managing the team.  I just don't think he can do that and take the offense where it needs to go all at once.