Hi M.,
I agree with Claudia T., so I probably won't be helpful to you, but try to cherish times like these, because I promise you they do grow up so fast! We have a 12 year old, and I can't believe the things I worried about when he was an infant (like when he would sleep through the night, introducing solids, etc.)
What I'm trying to say is that everything seems like a big deal when they're babies, but when you reflect back on it later, you realize that it wasn't really important in the grand scheme of things.
We have a 6 month old that we are just cherishing so much right now. He sleeps with us every night, and I am not going to worry about any little things this time around. You know that book, "Don't Sweat the Small Stuff"? That's the approach we are taking this time.
Do what you feel right about doing. If it's a problem for you that she sleeps on your chest, then by all means find a solution you can live with. But, if it's a problem for other people (ie mother-in-law telling you not to do that, etc.), politely thank them for their advice and then do what you want to do anyway. In the long run, you are the one who lives with your baby, and only you can know what is right for her.
Oh, and it's very normal for babies this young to want to be in constant contact with the mother. That is nature's way to insure their survival. So, she's probably not going to be happy about being separated from you. Every baby is different however. Our first one didn't mind being in his crib and always slept there. This one has never slept in his crib. We tried it in the beginning, but he always woke up immediately when placed in the crib, so we realized it wasn't a good option for him. Just follow your instinct and you will come up with a solution that works for your baby and for you.
I guess bottom line is do what makes life easiest for you :) If that means sleeping with the baby (within safety guidelines of course), then do that. If that means having the baby sleep alone, try that. She will be more likely to do this as she gets a bit older and is able to sleep more soundly (ie 6 months).
One more thing...our 6 month old slept on our chest at first too, but at this point he never does that anymore. So, it won't last forever. He now sleeps next to me, but not on me. So, it will get better soon :) Hang in there!
Good luck!
E. (mom to 4 blessings)