What's the best method for a man to permanently remove back, shoulder and chest hair?

You should do IPL hair removel, depend of how strong is your hormone, maybe can grow back, some people work fine, some not, other option waxing, do every 4 to 6 weeks, the hair become fine, some of my clients dont have hair like as before anymore.
waxing in Bromley

I would recommend Laser or Intense Pulsed light. If you have strong dark hair and pale skin, you should see results fairly quickly. Waxing will be an on going treatment and Electrolysis will take a long time to clear, as each hair follicle needs to be treated individually.

I would say IPL

IPL is not a laser and is significantly less powerful than a laser. Having said that, not all lasers give the same results. The best laser machines for permanent hair reduction available at the market right now are Lumenis LightSheer and Soprano (when the painless mode is switched off on the Soprano machine). Please, check out this article to get more info https://www.bodysilk.co.uk/news/2012/laser-hair-removal-vs-ipl

Their is nothing like permanent hair removel,its permanent hair reduction which is IPl or laser.and one fact is you can not wax during the treatment depandig on what machine is salon useing,coz you have to keep the root of hair to be burn and make the hair groth reduce.or reguler waxing like every 2 to 3 weeks will also reduce the groth of hair slowly.

Thank you for enquiring about Permanent Laser Hair Reduction . Intense Pulsed Light (IPL™) technology offers a gentle, non-invasive, long lasting solution to unwanted hair on the face, back, legs, bikini line or any other body area.
We have been carrying out this treatment for many years and it is very successful. We are registered under the Care Quality Commission (which is very important to know if you are looking and comparing clinics).
We are not the cheapest Hair Removal Clinic as we concentrate on the highest quality of treatment. With cheaper treatments some hair can be missed & we assure our patients that they will not have tufts of hair remaining untreated.
In order to offer treatment a few guidelines must be met. You cannot have a suntan, have used fake tan or sun beds a month prior to treatment as the laser light is attracted to the pigmentation in the hair, and so you may burn as the light would also be attracted to the pigmentation in your tanned skin. The use of St John’s Wort, and some medicines can make skin light sensitive and cause burns. Please bring with you a list of any medication that you may be taking. You cannot be pregnant at the time of treatment.
Pricing starts at £75 a treatment up to £250 a treatment depending on the area being treated. Please also keep in mind that we offer 0% interest financing for 6 months, 12 months or 2 years.
We would like to invite you to come in for a personalized consultation with one of our specialist nurses. They will be able to accurately assess you and give you the best treatment plan. Please keep in mind we have two sister clinics, one in Abingdon and one in Witney, should either clinic be more conveniently located for you please visit http://www.qutisclinics.co.uk.
We charge £50 for a consultation; however if you go ahead with treatment this amount is held on account and will be deducted from your first treatment cost.

Please call us on 01844 213007 or e-mail us at info@mbnsclinic.co.uk to make a booking or with any further enquiries.
We look forward to meeting you.

You will probably hear that is laser or electrolysis, but I can tell you that I have few clients who did that 4 years ago and now their hair are growing back, in patches, not as bad as before, but still coming back. I do Body Sugaring, which removes hair including roots and leaves skin beautifully soft and silk and hair are growing back thinner and weaker and period between treatment becomes longer, but still you have to do it 5-6 weeks if you want to keep your body "clean" and hairless. Good luck!

I guess the answer really hinges on your definition of permanent and how much you want to pay. I would always opt for waxing which will need repeating every 4 - 6 weeks. I will leave others to respond on the question of IPL and Electrolysis my own experience is that these treatments are not as permanent as is often portrayed.