I think Tunes pretty much said it all, but I wanted to elaborate a little. I've bought from large ranchers and I've bought from hobby breeders. With the large ranchers, it was pretty much hand over the money and you get your chin. The hobby breeders I've dealt with, some have required a simple form or two, some haven't.
As a personal example - we do rescue work, so we see our fair share of people wanting to adopt a chin. We require that our potential adoptive homes read our care packet and fill out an adoption form which asks questions about chinchilla care and the type of cage they have, type of food they plan on feeding, etc. Usually, the potential adoptive family has read the care packet and filled out the form (gets emailed to them and back) before they come to pick up a chin. The exception is when people want to come and decide if they want a chin - but then, those people still cannot leave with a chin without filling out the adoption form.
Assuming someone's emailed us and has read our care packet and filled out our adoption form to our satisfaction, they then come over, pick out their chin/supplies. They then have a pickup form they have to sign, which has the chinchilla's info on it (color, name, dob, sex, age, weight), basically agreeing that they're adopting that specific chinchilla, and we both sign the form. Then, lastly, since we're now on Petfinder, they require that we have an adoption contract that's completely separate from the adoption form, so we also have a 1 page adoption contract that basically states that the person will care for the chinchilla humanely, give it food/water, provide necessary vet care, yadda yadda, and return it to us if they cannot keep it... and they have to sign that. And THEN they can take the chinchilla home.
I prefer if people bring a carrier to bring their chinchilla home in. I really hate boxes for long car rides, and when we get people coming from 2 hours away.... they're not leaving with a chin in a box. However, the people who do live close... I will give them a box if they don't have a carrier to take their chin home in.
It sounds complicated... but in reality, I don't think it's all that bad.... I really do think that the people who really have the best interests of the chin at heart won't have a problem filling out a little paperwork.