My chime doorbell only works if the button is held down. Help.

? Don't you have to push the button on them to make them work? Can you explain better?

A doorbell circuit is rather simple. You press the butto and you get a chime. From your description of the problem I suspect the issue is with the contact inside the doorbell switch.

Easiest thing to do would be to repllace the switch before trying to get to the transformer and chime system (usually buried behind all matter of junk on the top shelf of a closet)

Here is a video of what needs doing from what you wrote. The only thing I will add is don't play with electricity, even low voltage. Take the time to shut off the proper breaker to the doorbell button.

https://www.bing.com/videos/search?q=How+to+Replace+a+Doorbell+Wired&&view=detail&mid=90CA2B943DBB1EDD97B790CA2B943DBB1EDD97B7&&FORM=VRDGAR