Update: This change ended up getting backed out, after it was discovered that it impacted smartcard authentication. Thanks for self-hosting Chrome Dev builds, IT teams!
A change quietly went into Chrome 59 that may impact your certificates if they contain non-ASCII characters in a TeletexString field. Specifically, these certificates will fail to validate on Mac, resulting in either a ERR_SSL_SERVER_CERT_BAD_FORMAT error for server certificates or a ERR_BAD_SSL_CLIENT_AUTH_CERT error for client certificates. The change that rejects such certificates is presently only in the Mac version of Chrome, but it will eventually make its way to other platforms.
You can see whether your certificates are using teletexStrings using an ASN.1 decoder program, like this one. Simply upload the .CER file, and look for the TeletexString type in the output. If you find any such fields that contain non-ASCII characters, the certificate is impacted:
Background: Certificates are encoded using a general-purpose data encoding scheme called ASN.1. ASN.1 specifies encoding rules, and strings may be encoded using any of a number of different data types (teletexString, printableString, universalString, utf8String, bmpString). Due to the complexity and underspecified nature of the TeletexString, as well as the old practice of shoving Latin1 strings in fields marked as TeletexString, the Chrome change takes a conservative approach to handling TeletexString, only allowing the ASCII subset. utf8String is a well-specified and well-supported standard and should be used in place of the obsolete teletexString type.
To correct the problem with the certificate, regenerate it using UTF8String fields to store non-ASCII data.