Before you start filling in the chip...
Use a section of a good clean microfiber/cotton towel with some Wurth Clean Solve:
Wurth Clean-Solve, (or equivalent)...applied to it to remove any contaminates (such as: wax, silicone, dirt, etc.).
This will ensure that the chip, and the area immediate surrounding it, is absolutely "ready" for your chip repair process.
Some very good suggestions have been offered on how to introduce the touch-up paint into the chip.
My tooth pick method for filling-in a paint-chip of the size you've described:
-Keep the vehicle out of the sun...work in the shade/garage/carport
-Tape off the area around the chip...trying to leave 'Just enough' of the exposed chip work-area
-Make sure the touch-up paint has a 'thin' composition (depending on the type of touch-up paint---should be on the label: either a paint thinner or paint hardener)
-Apply enough touch-up paint (via tooth pick) to the chip so it is nearly filled-up, but not overflowing.
-Wait a few minutes...Take another clean, "Wurth Clean Solve'd"-MF/Cotton towel, and gently swipe over the chip...you'll remove some of the touch-up paint, but don't worry...this will aid in
'pushing' the touch-up paint into every nook & cranny of the chipped area...as well as clean-up the surrounding area of any excess.
-Let this chip-repair-step...dry and cure for a few days (unless you have IR lamps to speed up this process)
-Repeat the above until there is but a miniscule gap (2.5mils

) between the surrounding, unharmed BC/CC and the chip...
(a square/flat-edge, and good lighting;
will assist you in detecting: this "sighting")
-Apply the CC to level..let it cure...Usually a gentle polish will be all that's necessary to make the repair gleam! Your "finale's" diagnosis may vary (YFDMV), though.
Hope your repair goes well...no matter the process you choose!! And don't rush!
Bob