Update May 5, 2018: Added waiting list information and the free transfer if you tested elsewhere. MyHeritage ran a campaign to provide 15,000 DNA kits to adoptees. The campaign closed recently with over 17,000 people signing up. Over the next 8 days, they will review the applicants to determine who gets the kits. You can read more about the process at https://blog.myheritage.com/2018/05/dna-quest-update/. MyHeritage is now up to 1.4 million who have tested or transferred their DNA results to MyHeritage.
There is a waiting list if you missed the sign-up date: https://www.dnaquest.org/. Also, if you tested elsewhere, you can usually upload your raw data from the other company for free to MyHeritage. Right now, 23andM3 v5 chip kits aren’t an option, but I expect they will be at some point in the not too distant future; earlier versions should be fine to transfer. If you tested with Ancestry DNA, FamilyTree DNA, you are able to transfer results for free.