I am interested in a new Chase card (50K Marriott) and possible other chase cards in the future. I currently have three open Chase cards (BA, CO and a Saphire). I'm not interested in keeping any of them open and would like them closed.

Is it better to close these cards before applying for the new one or is it better to apply, transfer lines around if needed and then close the previous three?

My credit is good. On a side note, I have received two Citi AA cards and a SPG card AMEX in the last couple of months if that matters.

Thanks