What are the DACs that use good circuits in the Audio sections?

chips, a concern?  Well, that is up to you.  I assume that if chips were SOTA, then Audio Research, Conrad Johnson and more would have pre and power amps that were all really big chips. 

 Chips/I.C. etc.  are in the ear of the beholder. 

I don't know of any DAC that doesn't have a chip or PCB in it. 

ARC preamp have chips in them to run switches, drive display, count tube hours... as do many many others including Aesthetix, the display is defeatable via the remotes for clearly better sonics. The Aesthetix Pandora DAC has an IMO stellar analog output stage ( as does the Lampizator... I own both )....

To make it a bit more clear, I am not talking of Chips/etc. in the units other operating parts, but in the audio signal path...what you hear, not what makes the display work. 

As mentioned above PSAudio, Chord and some others use software for the digital conversion but I have no idea if there is a chip somewhere in the signal path. They might use a chip on the digital inputs. CD player or streamer will have chips, not sure you can do digital and avoid using a chip somewhere in the audio path. If you stream from the internet there are chips in the modem that covert the analog to digital.