Can a wood-burning fireplace be installed in a condominium built in California?

Your first challenge will be to obtain a local building permit to burn wood indoors, which is generally prohibited in most areas of the USA unless that is your only source of heat during cold weather.

Next, read your governing documents to determine the level of design and materials documentation you must present to the association's board -- potentially the architectural review committee -- for their approval before you begin your renovation or installation.