If my iPhone charger broke will the apple store replace it

If the apple care includes replacement of iphone chargers, then they will. but it's best just buying a cheap one from either amazon or Ebay.

But here https://www.apple.com/uk/support/products/iphone.htmlit states that they can replace it if you have Apple care.

"With AppleCare+, you get repair or replacement coverage for your iPhone that includes up to two incidents of accidental damage, each subject to a £55 excess fee, and coverage against battery depletion of 50 per cent or more from original specification. Coverage includes the following:

• Your iPhone
• Battery2
• Included USB cable and power adapter"

But make sure to get apple care for Iphone, not for any other if your only wanting it for your Iphone.

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Don't buy cheap, non Apple chargers or cables. They don't adhere to the strict Apple specifications and there are too many reports of them not working correctly.

Depending on how long you've had the iPhone and if it's in warranty (less than a year old or you have the extended Applecare) it should be covered by Apple. More warranty info here: https://www.apple.com/legal/warranty/products/ios-warranty-document-us.html