Can a foreigner obtain Belgian citizenship by virtue of same-sex marriage to citizen Belgium?

Yes. According to the Belgian Nationality Code, a foreigner can obtain Belgian citizenship through naturalisation, which requires meeting certain conditions, including a language proficiency requirement and a residency period in Belgium. If a foreigner is married to a Belgian citizen, the residency requirement is reduced from 5 years to 3 years. Same-sex marriage is recognized in Belgium, so a foreigner who is in a same-sex marriage with a Belgian citizen would be eligible for citizenship under the same conditions.