Sounds like the wrong way since you are risking losing data on memcache.
You can write to one entity group once per second.
You can write separate entity groups very rapidly. So it really depends how you structure your data. For example, if you kept an entire chat in one entity, you can only write that chat once per second. And you'd be limited to 1MB.
You should write a separate entity per message in the chat, you can write very, very quickly, but you need to devise a way to pull all the messages together, in order for the log.
Edit I agree with Peter Knego that the costs of using one entity per message will get way too expensive. His backend suggestion is pretty good too, although if your app is popular, backends don't scale that well.
I was trying to avoid sharding, but I think it will be necessary. If you're not familiar with sharding, read up on this: https://developers.google.com/appengine/articles/sharding_counters
Sharding would be an intermediate between writing one entity for all messages in a conversation, vs one entity per message. You would randomly split the messages between a number of entities. For example, if you save the messages in 3 entities, you can write 5x/sec (I doubt most human conversations would go any faster than that).
On fetching, you would need to grab the 3 entities, and merge the messages in chronological order. This would save you a lot on cost. But you would need to write the code to do the merging.
One other benefit is that your conversation limit would now be 3MB instead of 1MB.