Air carrier Captain reported an NMAC during climb with what was possibly a UAS. No evasive action was taken.

Narrative

After take off and climbing we were talking to various ATC controllers and doing after-departure tasks. The airplane was having an issue with its LNAV button on the Mode Control Panel (MCP) which was distracting and required flying via HDG SEL. The First Officer (pilot monitoring) was copying down a radio clearance when I saw a black object coming into view straight ahead of us. Before I could even react I saw what looked like a large quadracopter drone fly past just off our left side. The First Officer noted he saw a blur flash by in his peripheral vision but didn't make it out.We were in the vicinity of the OAKEY fix climbing through 17;000' when the object flew by. It was square in shape and black and approximately 3 feet in diameter. I believe it had lettering on it but it went by so fast I couldn't make any of it out. It was extremely close and appeared to only miss the cockpit windows by a few feet. I'm pretty sure it went over the left wing as it was abeam our window height. The entire incident was so fast I didn't have time to attempt to maneuver before it was already past us. To say it was a rattling experience is an understatement.