The left speaker (earphone) is connected to the "tip" of the connecting cable. Ensure that you have fully inserted the cable at both ends. Also try plugging into another source of music etc to see if the problem still exists,
If inserted OK and another source makes no difference try the following:
With the headphones playing, very gently flex the cable where it leaves the plug and listen if the sound comes and goes in the left speaker. Do this at both ends of the cable if necessary. If it does you probably have a faulty termination in the cable connector plug. If the left speaker still makes no sound it could still be a faulty cable or faulty headphones
If you have an Ohmmeter you can check for continuity from one end of the cable to the other. You may have a faulty termination in the cable You should only have to check for continuity from the "tip"of one end of the cable connector to the "tip" of the other end, as only the left earphone is faulty.
If you haven't got access to an Ohmmeter or your tests don't prove anything you could try going to a Bose outlet and ask if you could try a cable. That way you will be able to prove whether the fault is in the cable or in the headphones.
If you prove that the headphones are faulty and not the cable, given that it is just over a year old I would still contact Bose and ask if there is anything that they will do for you. I think that they may be less receptive to a cable problem as opposed to a headphones one.