Will a rattlesnake chase a person down and bite them?

No. Snakes are not out to get you. To them, you are a large and potentially dangerous animal. Most snakes will avoid humans whenever possible - when they feel the vibrations of a large animal like a human approaching them, they will slither away. If they are taken by surprise, they will try to warn you off - this is the purpose of the rattlesnake's rattle. It's letting you know it's there. No venomous snake wants to waste its venom on defence - it needs it for killing prey. It will only bite as a last resort, and even then is capable of delivering a 'dry bite', in which no venom is injected. Most snake bites occur when the person is doing something stupid like trying to kill the snake or pick it up. If you leave them alone, they'll leave you alone.