Casa Chiara is the best apartment we've stayed in Ostuni (and we've stayed in quite a few now).
It's functional, stylish, minimalistic whilst having everything you need, spacious, strategically located in the centre of town whilst being away from the chaos and noise, and has a killer view over the sea and old town.
For those worried/complaining about the steep stairs to reach the upper floor: you'd be hard pressed to find houses in the centre of Ostuni that don't have steep stairs - it's just the way houses were built here. The ones at Casa Chiara are actually quite wide and not overly steep - there's definitely worse.
Paul is just a great host: very quick at responding, very flexible and accommodating at every request we had to make our stay even more comfortable than it already was.
If Casa Chiara is available for your dates, book it straight away - you won't regret it!