I put a little TSP in every couple of weeks. Catch it when it"s burned down to coals, stir them up just enough to get it drawing well and put a couple of tablespoons of TSP on the coals. I leave the bypass damper open for 5-10 minutes so that the chemical goes up the chimney.
I"d like to say that I went from having to clean 2-3 times a season to it not really looking like it needed cleaned when I ran the brush up it once a year, but I also burned it a little hotter* shortly after I started using the TSP and I"m sure that helped also.
*I have a flue thermometer on the stove itself (since the pipe is double-wall). I used to keep it in the 250-500 F range, but now keep in the 400-750 range). Also, we had a lot of (well seasoned) cottonwood and it"s probably more ash and "other" lately.