I chipped my front right tooth. How much does it cost to get this tiny chip repaired permanently? (photo)

Everything done in dentistry will eventually fail, just as these resins have.  Some things take longer to fail, so the associated costs will be more.  In this case, a bonded porcelain veneer instead of a bonded composite resin may last longer, and will likely cost $1000-2000.  A cheaper option would be to do yet another resin, but then wear a night guard so that you don't grind your teeth while you sleep.

In the photo you sent, the chipped area doesn't seem large but fractures of this size and location can be a bit tricky depending on your habits (chewing nails, ice, grinding your teeth, etc) and depending on how you bite on this tooth. If a filling is done in this area, without insurance, it can run anywhere from $150-300 depending on where you live. If you have a filling done several times and it keeps coming off, you may need a more aggressive treatment, such as a veneer, that will be longer lasting. No matter what treatment is done, a careful evaluation of your biting, grinding, and chewing habits will need to be done to ensure that the restoration does not fail. Hope this helps!

Believe it or not, small chips are not easy to repair. Bonding, the procedure of colored filling material applied to the tooth, can only adhere well to larger surfaces. That is why small chips sometimes break off when eating, or if the bite is not carefully adjusted to avoid the lower teeth from hitting it, cause easy breakage.
So this is a loaded question. First, a thorough bite examination is needed to see how the other teeth hit this edge. AND how did this chip occur in the first place? If it came about from wear or interference from other teeth, a few additional steps are needed. Adjusting the interference to avoid the chip, and possibly creating a small "preparation" into enamel to get more area to bond to.
A knowledgeable cosmetic dentist performs all of these steps and tests automatically to increase the chances of the filling staying a reasonable amount of time.  Even so,  a few replacements of a small chip over the years should be anticipated. There is a lot of wear and tear from eating, and tooth movement on a tiny bonded area. So larger breaks may be easier to repair than small ones!
Lastly, if the color and or shape of the teeth are also poor, or there are other large fillings, a porcelain veneer will remedy all of the problems at once.
So cost cannot be determined. one chip is not the same as the next!

This tooth could be repaired with wither bonding or a porcelain restoration. These vary quite a bit in fees based on the city you are in, with the porcelain veneer/crown being more expensive. check with your local dentist or this website does provide average costs per treatment based on location. 

Contrary to what is look like (such a small defect) but these chips are the worst to repair.  Most common method is white fillings.  Down side to that is since it's such a small area, the white filling will break off months later with more tooth structure break off with each time a new white filling is placed.  Fast forward 5-10 years, that tooth will be crowned or veneered.  The most durable to repair that chip is a crown or veneer.  It just unfortunate to spend so much money on such a little defect.  Remember, you read it here first.  White filling will not hold or last on these type of chips.