What carrier do you use? I use Verizon and also notice this same issue. However, if I open one of the other SMS apps on my phone, such as the stock messaging app, Hangouts, etc, the messages do show as delivered.
I emailed Chomp support and was told that it is because the carrier doesn't send the report as requested. I responded with the above info about being able to see them as "delivered" in any other app I use, but Chomp only ever shows as "pending". They said that I need to not use other apps. So, their support for this is basically non-existent. They know about the issue and they know it is related to their app only, but don't seem to care I guess....
Kratos