Conrad was Ray's "pet" chicken that made his first appearance in Let's Play Minecraft Episode 83 - Geoff's House Part 2 towards the end of the 34th minute mark. Initially name Candice by Ray, the chicken was seen shortly after Ray died due to falling from the top of Geoff's house and spawned back in his hut. Though not a certainty, it can be safe to assume that the chicken was a result of a random spawn in the cauldron itself since it makes a sudden appearance in front of Ray and was not there right before that. It was sheer luck that Ray was looking directly at him when he spawned, though he didn't acknowledge him till a few minutes later.
Since then, it became a part of Achievement City as a pet and another animal safe from Ryan. But for how long? In Let's Play Episode 89 - Mad King Ryan Part 1, Ray discovers that Conrad is not in his cauldron anymore and has gone missing. Moreover, there was a new addition to Ray's house: Percival the Ocelot.
The disappearance of Conrad is a mystery. By instant speculation, Ray believe Conrad probably died or despawned. As far as despawning is concerned, chickens cannot despawn if they are in an area no bigger than 20 blocks in any direction. Given the size of Ray's house and the fact that Conrad was trapped in a cauldron, this seems unlikely. The other alternative is that Conrad died. The mostly likely reason is Percival. Ocelots kill chickens and it is very possible that Percival (who is not a tamed ocelot) murdered Conrad. In fact, it is possible that Conrad was what attracted Percival to Ray's house in the first place. However, we cannot ignore the fact that Achievement City is under the rule of a Mad King, who is about to enjoy is Third Reign after winning King Gavin. After losing to Gavin in Shopping List due to his failure to find a single chicken, Ryan developed a hatred for chickens. Ray would never have been able to save Conrad. And as we saw with Edgar's hole, Ryan has done things in Achievement City without the knowledge of Geoff or Gavin.
No matter what happened, he was as much a part of Achievement City as Ray was and will be missed. R.I.P Conrad.