I don't know of an OEM tool kit with anything to help with a chain adjustment.
My Honda tool kit was a Philips screw driver and a cable with two loops to secure your helmet to your NC (I actually use that when riding out of town with my wife)
I would recommend building your own kit, especially if your in a time crunch.
There are some slick portable tools but most are expensive and only ok, especially if they're used as a primary to for removing or adjusting the rear tire as an example.
Road side tools are designed for being light and compact, not for being the best or a long lasting tool.
That said you'd need to carry two large wrenches and two normal sized wrenches just to adjust your chain, so if space is at a premium or if your worried about weight (an unlikely problem) then you should get road side tools designed for the job