There's many different ways race timers charge for chip timing services. Some will charge a simple per-participant timing fee (subject to a participant minimum), others will charge a minimum starter fee that includes a number of participants with a per-participant surcharge for every participant beyond the number the starter fee covers.
Typically, for gun time results (=race timed at the finish line only using a common start time) you should expect to pay around $500-$700 plus $1-$1.50 per participant. For additional timing points, either at the start or at intermediate checkpoints, add $300-$500 per timing point.