It's so easy to do. There are 3 types of travel chopsticks that I am aware of. The first pictured here is a plastic box with a sliding lid and only costs a few dollars.
This type of travel container comes in two sizes, standard and slightly smaller.
It weighs almost nothing and is so easy to just toss into your purse or keep in the glove box of your car. After each use just wash, dry and place back in the container for the next time. I've carried variations of this type of case for years.
This year I found a more compact and elegant case.
With a hinged lid and a demi pair of chopsticks inside it fits into my smaller purses because it doesn't take as much space as the standard length black sliding container above. It's hard to see in the photo but the last few inches to the tip are slightly textured so that you can hold food more easily with them.
And the fanciest of all are these Collapsible Travel Chopsticks (on the Think Geek website) that you actually screw together for each use. Also far pricier at $30 - $40 I haven't been tempted to get a pair like this because I'd probably lose them, break them or forget them at some restaurant and they'd get thrown away.
At $5.25 this plastic collapsible style is probably more my speed.
For me it's just one small effort I make to be more earth friendly :)