We develop a method for fabricating very small silica microbubbles having a micrometer-order wall thickness and demonstrate the first optical microbubble resonator. Our method is based on blowing a microbubble using stable radiative CO(2) laser heating rather than unstable convective heating in a flame or furnace. Microbubbles are created along a microcapillary and are naturally opened to the input and output microfluidic or gas channels. The demonstrated microbubble resonator has 370 microm diameter, 2 microm wall thickness, and a Q factor exceeding 10(6).