You have to give 30 day's notice to change terms, and the 30 days has to coincide with the day rent is due. So you could give notice December 1 to be effective December 31. It has to be in writing.
If you know that this dog is killing chickens and biting people, have you advised Animal Control? They have a strict protocol for dealing with dangerous dogs.
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I agree with Ms. Powell and the lack f control of her dog maybe be a liability for you and take all steps necessary to protect yourself and hopefully your lease has a nusiance provision and you can give her notice to cure the problem or end the lease.
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Having a vacant house sometimes is better than having a bad tenant, especially one that is not paying rent on time and has a dog that "kills chickens and bites people". One or more of the victims may sue and name you as a defendant.
Sure, if you go through the statutory steps, you can require the tenant to pay by cash or cash-equivalent and get rid of her dog. However, she may just move out. If you accept payment in cash, you will need to give the tenant a receipt for the cash.