You can chase him to you heart's content - the content of one heart. But you can chase each other to your hearts' content - the content of both hearts.

Heart's content, assuming only one person is being addressed. http://www.phrases.org.uk/meanings/hearts-content.html

That's the problem with these questions. I assume it's taken from one of your practice books? They tend to annoy students with this kind of stuff. As if this is the most essential question you can ask someone who's learning English. Again, as said by Claire and Susan612, the answer can be heart's content or hearts' content depending on whether the person being addressed was intended or both of them. The thing is, since English doesn't distinguish between singular you and plural you, both could be correct. I'm assuming, from this snippet, that the person being spoken to is a police officer and he is persuaded not to arrest the other guy (the groom I guess) during the wedding. (Biggest day of my life, probably a wedding.) Now, I don't see why a thief/murderer would be chasing a police man, which would lead me to say "heart's content". But then again, perhaps they're old buddies gone off on different paths later in life and still have some sort of connection, so the bride feels she can asks this of the police officer (which normally isn't what happens). In that case they probably have an intricate relationship, and the whole chasing each other thing makes more sense. So then I'd say "hearts' content". If someone pointed a gun to my head and asked me to pick one I'd pick the latter.