Two things that jump right out to consider is your ratio of acid to alkaline producing foods and a potential allergy.
I ate 100% Paleo and resolved long-term GERD. Every now and again though, I would get an episode of heartburn. Testing ended up showing sensitivity to eggs, tomatoes, and carrots - all which were staples of my diet. Although both foods you ate are relatively low on the allergen list, I do have a buddy who is sensitive to chicken.
With regards to acid-base balance, I tell people to use the palm size guideline for protein and then put the other hand next to it and that's the minimum amount of veggies you should have. In other words, a handful of meat, and two handfuls of veggies.
You also could be experiencing some rebellion by nasty gut flora or a candida overgrowth as you begin to starve them of their sugar smack. You may want to consider a high-dose probiotic intervention for a week or so and then taper down to a maintenance dose or up the fermented foods.