Omicron variant (B.1.1.529) infections are rapidly expanding worldwide, often in settings where the Delta variant (B.1.617.2) was dominant. We investigated whether neutralizing immunity elicited by Omicron infection would also neutralize the Delta variant and the role of prior vaccination. We enrolled 23 South African participants infected with Omicron a median of 5 days post-symptoms onset (study baseline) with a last follow-up sample taken a median of 23 days post-symptoms onset. Ten participants were breakthrough cases vaccinated with Pfizer BNT162b2 or Johnson and Johnson Ad26.CoV2.S. In vaccinated participants, neutralization of Omicron increased from a geometric mean titer (GMT) FRNT50 of 28 to 378 (13.7-fold). Unvaccinated participants had similar Omicron neutralization at baseline but increased from 26 to only 113 (4.4-fold) at follow-up. Delta virus neutralization increased from 129 to 790, (6.1-fold) in vaccinated but only 18 to 46 (2.5-fold, not statistically significant) in unvaccinated participants. Therefore, in Omicron infected vaccinated individuals, Delta neutralization was 2.1-fold higher at follow-up relative to Omicron. In a separate group previously infected with Delta, neutralization of Delta was 22.5-fold higher than Omicron. Based on relative neutralization levels, Omicron re-infection would be expected to be more likely than Delta in Delta infected individuals, and in Omicron infected individuals who are vaccinated. This may give Omicron an advantage over Delta which may lead to decreasing Delta infections in regions with high infection frequencies and high vaccine coverage.