It comes as no surprise that autochthonous chikungunya has occurred in Florida. The simple maxim that must be kept in mind with respect to vector borne diseases is: if a competent vector exists in areas in which imported cases are occurring, it is only a matter of time before local vector populations contract the pathogen.
Florida is an area hospitable to Aedes mosquito and has been plagued with locally-transmitted dengue for several years. As chikungunya shares many of the same characteristics of dengue, it is no surprise that it has found welcome in Florida.
Intensified efforts to control the vector, which is already ongoing for dengue, will likely occur. However, it may be exceedingly difficult to eradicate chikungunya if it has thoroughly settled in local Aedes population.
For a great overview of these issues see this recent NEJM piece by Fauci and Morens.