Section breaks, in all likelihood. They don't need to be long on DC systems, but are long on AC system phase gaps, with an insulated section in between to prevent arcing, and pop the breakers if there is any (since it'd be a phase to phase arc). Breaks where the phase is the same on both sides on AC systems can be short ones like DC.
The catenary is sectioned so that parts can be protected seperately, much like your house has a bunch of breakers - imagine if you only had one, and everytime you overloaded anything, it popped...
There's two ways sections are done. The most common is an insulated piece with arc horns in the wire. Both AC and DC systems use this.
The other way is to raise the wire up up up above the pan's reach, and then come back down - this is done on some drawbridges, mostly noteably Cos Cob on the New Haven line (NEC). The pan litterally comes off the wire, and 'flys' in the air as the car goes accross the bridge, then comes under the wire and the wire drops down. A lot like a third rail gap.
The New Haven's pans didn't reach as high as the PRR ones did, and ledgend has it, the first GG-1 above New York got hung up at Cos Cob. I don't know about Chicago, but out east, there are some wild variations in wire height - the PRR had 'high wire' and 'low wire' signs to indicate extremes to the crews, as there were restrictions on operating at both (most noteably, not to drop the pan in low wire territory, as there wouldn't be enough space to break and arc, and high side circuit breakers on rail equipment are a recent innovation.)