Technically no, since many plants (and I'm sure peppers are included) will grow into whatever pot you put it in. I've got mine in 6" pots right now. Granted, it's a bit on the low end of what a pepper plant should be, but I had little choice due to the limited space in my apartment. Most people swear by pots that will fit 1 gallon. As was recommended to me, and recommended to others, make sure not to overwater or overfertilize the plant. Just use the recommendation on the fertilizer's bag, and for water, the rule of thumb I use is that on average, the soil should be roughly as wet as a damp sponge a few hours after using it.