The globally-circulating SARS-CoV-2 Variant of Concern Omicron (B.1.1.529) has a large number of mutations especially in the spike protein, indicating that recognition by neutralizing antibodies may be compromised. We tested Wuhan, Beta, Delta, or Omicron pseudoviruses with sera of 51 participants that received two or three doses of the mRNA-based COVID-19 vaccine BNT162b2. Following two doses, sera had >22-fold reduced neutralizing titers against Omicron compared to Wuhan pseudovirus. One month after the third vaccine dose, Omicron-neutralizing titers were increased 23-fold compared to two doses, with titers similar to Wuhan-neutralizing titers after two doses. The requirement of a third vaccine dose to effectively neutralize Omicron was confirmed using live SARS-CoV-2 in a subset of participants. These data suggest that three doses of the mRNA vaccine BNT162b2 may protect against Omicron-mediated COVID-19.