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Mrs Q had her tooth chipped when the knoecked her out for he C-section. It's one of her front teeth and has taken the corner off it. I presume it was when the pipe thing got shoved down her throat.
She doesn't care that much about it, yet I know that to fix it will cost some wedge.
Will the hospital cover the cost of fixing it or not?
Free dental care if your preggers and for 12 months afterwards IIRC.
May not need fixing, I've chipped a couple, dentist thinks they're fine and I'm sure he'd fix them if they needed to be. Only issue may be cosmetic.
I've chipped my teeth, more chewing torque and speed..... 
Will the hospital cover the cost of fixing it or not?
Unlikely - if she was getting C-section under general anaesthetic it was likely in order to save your wife/child's life. The consent form that she signed (assuming she was well enough to do so) almost certainly acknowledges the risk of minor dental damage (it is a known 'complication' (one in a few thousand?)). I had a pair of glasses broken during GA (I don't know the exact circumstances, but they were intact when I went into theatre and returned to me mangled and with an apology when I came round) and it never crossed my mind to claim them from the NHS.
As j_me says though if it is required for dental (rather than cosmetic) reasons it will be FOC on the NHS during the 12 months after the birth.