Long answer: No, but if you plan on using your insurance for paying for your Chiropractic care/treatment then in some cases, you may be required to get a referral from your primary care provider (the family doctor under your insurance plan).
I however know that sometimes the primary care provider is basically a bit under the thumb of the insurance company. An insurance company will sometimes cut a primary care provider off if he/she is referring patients out too often for "non-traditional care' or not seeking more affordable treatment options. Prescription medications are an example. They are expensive but a lot less expensive than 3-4 trips to the Chiropractor or 1 trip to the Acupuncturist.
This is a tough economy and a tough financial world especially for doctors. And it is easy to fall in the trap of "doing things for economic reasons". I feel that sometimes, primary care providers, have their arms being twisted to "refer" in the direction the insurance company desires. This may or may not be true but I've been in practice for 17 years in Bellevue, get great results, have raving reviews on-line and in the community and have had only 25-50 referrals in 17 years from a primary care providers. That tells me that there is an effort somewhere, to steer referrals off in another direction than alternative care. I don't know where that is coming from but I'd hope it's not from the physician's themselves.
Anyone can come to the Chiropractor at any point for any reason with or without a referral. Most of my patients are rebels and just skip the insurance allowance game and pursue Chiropractic even if it's not covered under their insurance plan. There's no safer way to treat your spine and musculoskeletal issues than with Chiropractic.
If your Chiropractor finds out that you need a referral before the insurance will pay out anything then the Chiropractor can help you find a local primary care provider (if you don't have one already) and help get the referral you need.
Once you've gone to a Chiropractor 1-2 times and experienced some relief...your physician is likely to advise you to keep it up and make a recommendation to continue. If however, you haven't seen the Chiropractor for your pain and you go to the physician he/she may or may not recommend a Chiropractor.
There are popular recommendations and "off the grid" recommendations. If a physician has found that people balk too often in going to a Chiropractor (even if the physician had his/her own good experience) he may not recommend a Chiropractor. People are usually more happy about getting a pill for their pain rather than seek out an alternative pain relief system that may take longer to achieve results.
However, if a patient is adamant about receiving a particular kind of therapy (such as Chiropractic) then the physician will usually go with the patient on it. Afterall, Chiropractic is more affordable, all-natural, less-invasive and has less long-lasting effects like drugs or medication or surgery. I have to believe, as a Chiropractor, as an alternative medicine practitioner that physicians would lean more toward natural, less-addictive, less-invasive therapies rather than straight-out recommendations for surgery and medications.
If your insurance demands a referral or doesn't allow for Chiropractic coverage then say something and report it to the company in writing. Enough complaints will turn the tides some day. Chiropractic is far less expensive in the long-run than other invasive medicines, drugs, surgeries. Drugs have side-effects and require further drugging to keep the side-effects at bay. Surgery permanently alters the form of the body structure and that throws the body out of whack and surgery also, usually, leads to more surgery.
The best thing to do is to wing the expense of the first visit, see your Chiropractor first and then work out how to best get the insurance company to help you, the insurance policy holder, get what you really need - healthy, natural care.
