The gemara[1] presents some of the rules for the kli[2] used for netilat yadayim, including that it must be able to hold a revi’it[3] of water. Potentially pertinent to your question, the gemara states that a utensil is unfit for this use if it has a hole the size of koness mashkeh – i.e., big enough not only for water to seep out through it, but even for water to seep into the cup through it.
There is a machloket Rishonim as to the reason for the disqualification of a kli with a hole.[4] According to the Semag,[5] a cup with a sufficiently large hole is not considered a kli (utensil) with regard to various halachic matters, including netilat yadayim. According to the Rosh,[6] however, such a cup is generally considered a kli, but the area above the hole is considered to be beyond the kli-like area, as the cup does not reliably hold water above that point. The problem, according to the Rosh, is that the water for netilat yadayim must be poured onto the hands directly from the walls of the kli.
One practical difference between these opinions is whether one may use such a cup if he pours the water onto his hands from the hole itself, rather than from the top of the cup (assuming that the cup can hold a revi’it up to the height of the hole). According to the Rosh, this is acceptable, because one is pouring from the top of the kli-part of the cup. According to the Semag, however, the cup is totally lacking in kli-status due to the hole, and it does not matter how high the hole is or from where the water is being poured. The Shulchan Aruch[7] rules leniently like the Rosh that one may perform netila through the hole. However, many Acharonim are machmir if the cup is made from pottery/ceramics, in which case it is not considered a kli if it has a hole.[8] (We assume your cup is ceramic, as metal and plastic cups rarely “chip.”)
If your cup has only small chips on its rim, it is hard to believe that this would disqualify the cup from being considered a kli, as such chips do not, in any serious way, impede the use of the cup to hold liquids. On the other hand, as opposed to the case of a hole in the middle of a cup, in which one can pour in such a way that the water will pour out through the hole alone, from where should you pour the water using your chipped cup? If you pour it randomly, or if you pour it purposely from the area that is not chipped, then you are pouring from a place that extends beyond the height of the complete circumference of the cup. According to the Rosh’s view, this is problematic. The Mishna Berura[9] rules that while it is not ideal to use a cup with a piece missing on top, if that is the only available cup, one should pour out from the chipped part, which is now lower than the rest of the top. Practically speaking, however, unless the chip is broad or deep, it will be difficult to pour only or even mainly through the crack.
The following idea may help. The Eshel Avraham[10] writes that if the height of the cup is not uniform, but that fact is not clearly recognizable to the eye, one may pour from the higher side. His primary logic is that “the Torah was not given to angels,” who can be exact, but rather to imprecise humans. He also points out that in any event the surfaces upon which a cup normally sits are not exactly straight, making the top regularly on an angle, such that a slight difference in height is meaningless. Piskei Teshuvot[11] writes that the same is true for slight height differences due to chips. However, it is difficult to present a clear rule as to how far one may take this comparison. If there is only a slight dent in a plastic or metal cup, it is indeed difficult to tell the height difference. Regarding ceramics, however, it is much more common for even small chips to make the area of the chip noticeably lower than the area right around it.
Therefore, in general, the best thing to do with a chipped ceramic netilat yadayim cup is to insert filler material to more or less remove the defect and the height change caused by the chip. Although some sources are quite particular about the material used as filler,[12] the practical ruling is that anything that works securely is fine.[13] Until this is done, there is room for leniency if the “hole” that is produced is barely noticeable.