Can a person be a police officer if they only have one eye?

There is no simple answer to this. First, you need to check any rules or eligibility requirements for police officers/sheriffs for this department--if the rules state, for example, that someone needs to have  a certain level of vision which this Chief does not or cannot have, that might be grounds for his removal. Then, however, you need to deal with the fact that under employment discrimination law, it's illegal to discriminate  against the disabled; reasonable accomodations must be made. Therefore, there's a good chance that it would be considered discrimination to not let the Chief have his job, though possibly the accomodation should be that he only does "desk" work, not field work, if he can't effectively pursue criminals.

Short answer: unless there is an eligibilty requirement that requires two eyes, it's very unlikely there are any grounds to remove him--and even iff there was such a requirement, it might run afoul of anti-discrimination law. Given how strong anti-employment-discrimination law is, it might be best to deal with this "politically" by voicing concerns to the appropriate legislative and executive officials, getting resident signatures on a petition to do something about the situation (which might mean restricting him to desk jobs), etc.