Is a carbon chiral it two of its groups are cis - trans isomers?
Any time all four groups bonded to carbon are distinct, including any sort of isomeric groups, you have a chiral center.  Comments associated with the related question referenced by @Loong indicate that the cis vs trans scenario is even included in the $R$ vs. $S$ naming convention.  This case is an $S$ configuration as the cis group takes second place and is counterclockwise from the hydroxyl group in the appropriate view.