"I had a really good day. It was nice to feel that all the work I did paid off," said Millar.
"I think I'm going to be better than anyone's ever seen me before."
Although he was pipped by Team Columbia's Kirchen in the final minutes, Millar will have plenty of confidence going into Wednesday's flat 232km stage from Cholet to Chateauroux, the longest of the 2008 Tour.
Overnight leader Romain Feillu - who took the yellow jersey after a dramatic stage on Monday - finished nearly five minutes behind Schumacher.
Cadel Evans - one of the pre-Tour favourites - had a good day in the saddle, finishing behind Millar in fourth with a 64-second overall advantage over rival Alejandro Valverde.
Americans Christian Vandevelde and George Hincapie also had good days on day four, finishing sixth and seventh overall respectively.
Team Columbia's Mark Cavendish finished over four minutes behind Schumacher in 143rd place.
Stage four results:
1. Stefan Schumacher (Germany/Gerolsteiner) 35 minutes, 44 seconds
2. Kim Kirchen (Luxembourg/Team Columbia) +18 secs
3. David Millar (Britain/Garmin Chipotle) same time
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