By Obama, but he was required to pick a Republican for the slot, so McConnell made the recommendation (and would've likely filibustered anyone he didn't approve of). Trump made him Chairman.
> The commission is made up of six members, who are appointed by the president of the United States and confirmed by the United States Senate. Each member serves a six-year term, and two seats are subject to appointment every two years. By law, no more than three commissioners can be members of the same political party, and at least four votes are required for any official commission action.
(Legally, I suppose he could've nominated someone from a third party for the slot, but practically that would've died with McConnell in the Senate.)
The independent-commission rules mandating partisan equality have always struck me as constitutionally dubious, at best. But after a lazy search, I can't find really any discussion of the topic.