Recently I have done very little model building because of all sorts of reasons, but now I finally finished the building process of my Tiger and gave it a couple layers of primer.

It will be an Early Tiger in Tunisia, used by the sPzAbt 501. Now from what I've read, the Tigers in Africa were painted in "Africa brown", but the Tigers from the 501st were resprayed olive green in Tunisia.

Now this may be a stupid question, but please note I'm still a beginner, and will be doing chipping for the first time Should I make the chips with the Africa brown color, or would the African brown paint on a real vehicle be chipped on the same places too? I don't want a heavily chipped look, though, only a little bit

Hi Paul. If your not after a heavily chipped vehicle use the "Africa brown colour", apply it in areas that would receive a lot of rough treatment,mud guards,raised surfaces and sharp edges,running gear and places the crew would walk on a lot.

For heavy chipping and wear on vehicles there is a method involving hair spray, if you do a search on here you'll find information on it, i haven't tried it myself and it would take some practice but it gives great results.
Good luck with your Tiger!
Cheers,
Tim

Colors for North Africa are a bit confusing, as the regulations called for tanks to have a two-tone cammo finish, but the colors were changed halfway through the Africa campaign, so a total of four colors were authorized (and some late arriving equipment in 1943 might have been painted in the new Dunkelgelb color).
The Tiger from the 504th Battalion now preserved at Bovington was stripped when the museum restored it, and they discovered that the original colors were from the 1941 scheme, rather than the 1942 scheme (old paint was supposed to be used up first). It's anyone's guess whether all the Tigers received these colors or if some had the later scheme. The restored tank has been repainted in modern paints matching the original colors.
The story of olive painted Tigers probably originated in the US Army's Technical Intelligence report filed by Colonel Jarrett, who examined wrecked Tigers in North Africa, which reported the color to be "green." German veterans interviewed by Wolfgang Schneider for his "Tigers in Combat" book reported that they used captured US paint to repaint their tanks, but this was a recollection offered over half a century after the fact, and may have to be taken with a grain of salt. Color photos of a group of demolished Tigers available in the Life Magazine online archives do not show olive paint (however, one of the authorized tropical colors was a bit greenish, possibly explaining Jarrett's report). On the other hand, perhaps the Germans did repaint them, but sometime after the Life photos were taken. It's one of those issues we'll probably never settle for sure, so take your best guess.
As for paint chips, the first tanks rushed across in 1941 were hurriedly repainted in the field, and the paint flaked off quickly, but the tanks shipped later were professionally painted, either before leaving Italy or at the factory, and the finishes showed comparatively little chipping. If the tropical finish was applied at the factory directly over primer, the chip would likely take the primer with it, leaving a dark spot of bare metal which would rust slightly. If the camouflage paint was applied over Dunkelgrau, the bottom layer of paint might or might not come off.
For a list of German military colors and hobby paint matches, visit http://www.miniatures.de/colour-ral-farben.html