It's definitely possible. It certainly isn't easy, but you can find independent pharmacies thriving in areas that have chains all around them.
You have to separate yourselves from them by offering better customer service (delivery, personal knowledge, etc.) and unique services (immunizations, medication therapy management, compounding, etc.). The start-up costs are high, but local wholesalers and organizations may be able to help you with getting your feet on the ground. One of the posters here, DoctorM, just opened up his own independent right down the street from a chain pharmacy. If you read the trade publications, you'll see all sorts of independent pharmacies thriving with unique business models.
If that's what you want, then go for it.