No, ChilliDB does not set any limit.
All of this is independent of ChilliDB and you should check your SMS carrier. The following is general advice only.
The maximum number of characters for a SMS message is generally 160 in GSM supported character sets (i.e. the standard ASCII characters one would normally use day to day). If you enter a character that is not supported, the format of the message will change to Unicode so the length will be less, however this all depends on your carrier and how they handle it.
The way SMS works these days generally is less strict - if you type a longer message it will be broken down into two or more text messages (depending on the length of the message) and you will be charged accordingly by your carrier.
You can track your usage and the amount of SMS partitions per message via the 'Manage ChilliDB SMS' screen accessed through the system management menu