No, it doesn't have a chilling effect because pharmaceuticals are a global market. The dirty little secret is that the US having crazy rates like "$2000 for two ibuprofen" as mentioned in another anecdote in this thread is exactly what enables price fixing in most of the rest of the world to be functional.

The disaster that is the US healthcare system is architected to eliminate any concept of price transparency to directly confound free market processes, and is costly to line the pockets of middlemen and pharmaceutical and medical/biotech firms, because their pockets aren't being lined elsewhere in what is an essential and large global industry. The US effectively subsidizes healthcare around the world by paying out the nose, and the entire thing is perpetrated against the American people by intentionally introducing smoke and mirrors to the process.