For example, I can look up what a companies stock price was like in the past, but I can't look up an option chain from the past.
Yes, past option prices are available for many options, but as far as I know not for free. You can get them from, for example, OptionMetrics. Probably there are other providers as well, which may be cheaper for an individual or small institution.
OptionMetrics data comes from the National Best Bid and Offer. Probably there are some over-the-counter options that are not included here, but for someone asking this question, OptionMetrics will most likely have the option you are interested in.