To do this, a special component called a SIDAC is used. This is a silicon device that blocks conduction, until a specific threshold voltage is reached, at which point it suddenly conducts fully, until current flow stops. It's similar to how a spark gap works.
To use one of these with an IC, a high voltage supply is used to charge a decent sized capacitor, and when
a threshold is reached, the SIDACs fire, dumping the energy through an ignition coil primary. The secondary then gives a pulse of around 40kV. ICs are not designed for this type of use, so could die, but most are usually ok for sparks of around 3 inches, as long as extra insulation is provided (PVC + silicone around the Hv terminal).
The circuit is really simple (assuming you have an HV supply already):
I used a pair of microwave oven capacitors for it (hence 2 in the circuit). Each SIDAC is rated at 240v, and I have 8 in series, giving a voltage of almost 2000V into the coil primary. The HV supply is a simple flyback. In the video below, I also show it with a microwave inverter supply, giving a much higher spark rate.
More pictures showing sparks to a light globe, and a video: