Almost every E36 engine runs a maintenance-free timing chain with no scheduled replacement — the M42/M43/M44 fours and the M50/M52/S50/S52 sixes all use one.
The single exception is the M40 (a SOHC 8-valve four sold outside the US), which uses a timing belt that must be changed about every 30,000 miles or 3 years. It's an interference engine, so a snapped belt bends valves.
Ignore the common "the M42 has a belt" myth — that was the earlier E30 application; in the E36 the M42 and M44 run a dual-row chain.