Why is it that in Deuteronomy 32:35, the ESV reads "Vengeance is mine, and recompense (i.e., the noun form for repayment of vengeance)...," while the NIV reads "It is mine to avenge; I will repay..."? The difference in the second part is not due to translation style, but to a complicated set of textual variants in the beginning of this verse. The Massoretic Text (MT) for this passage reads לי נקם ושלם "Vengeance is mine, and recompense." The Samaritan Pentateuch (SP) reads instead ליום נקם ושלם "On the day of vengeance and recompense." The Septuagint (G) reads εν ημερα εκδικησεως ανταποδωσω for ליום נקם אשלם "On the day of vengeance, I will repay." Romans 12:19 and Hebrews 10:30, on the other hand, read εμοι εκδικησις εγω ανταποδωσω for לי נקם אשלם "Vengeance is mine, I will repay." There is one Qumran fragment 4QPaleoDeut(r) frg. 41, which contains on line 2 the top tips of the letters לי, and even though the text is not extant at the point in question, the editor (Skehan) claims that the traces below line 1 best fit the word ליום "On the day."
4QPaleoDeut(r) frg. 41 from DJD
Thus, all four possible combinations of readings for these two phrases are attested in ancient witnesses, a perfect example of how there were numerous textual differences even in early times. How do we resolve the differences, since there is ancient support for each combination of readings? The key is to recognize that these phrases together form a parallelism with the following לעת טמות רגלם "In due time their foot will slip" and that the variants must be evaluated together.
SP's ליום נקם ושלם "On the day of vengeance and recompense" is grammatically strained, as it lacks a main verb, and also has no verbal parallel with the following clause, so it is intrinsically unlikely. The NT's εμοι εκδικησις εγω ανταποδωσω for לי נקם אשלם "Vengeance is mine, I will repay" is parallel within itself, and thus cannot function as a proper parallel in the context of Deuteronomy, where it would have to function as an awkward parallel within a parallel.
This leaves MT and G as possible candidates. לי נקם ושלם "Vengeance is mine, and recompense" is a complete sentence and grammatically tenable in combination with the following clause, but the parallelism is formally poor, even though one could argue for some sort of synthetic parallelism. Fortunately, one need not resort to this explanation, as G proves itself to be intrinsically the superior reading with its εν ημερα εκδικησεως ανταποδωσω for ליום נקם אשלם "On the day of vengeance, I will repay," which makes for tight formal, synonymous parallelism with the temporal adjunct and main verb of the following clause.
The reading ליום נקם אשלם "On the day of vengeance, I will repay" easily explains all the other variants with simple text-critical explanations, so there is no reason to doubt the originality of the G reading. The ום of ליום נקם was accidently dropped off the end of the word when the scribe confused it with the final ם of נקם. The א of אשלם was replaced by ו by simple scribal error and/or as a secondary correction to better correspond to the variant לי נקם.
Thus, Deuteronomy 32:35 probably originally read with the Septuagint ליום נקם אשלם "On the day of vengeance, I will repay...," rather than the לי נקם ושלם "Vengeance is mine, and recompense" of the ESV or the לי נקם אשלם "It is mine to avenge; I will repay..." of the NIV. This is a fine examlpe of how formal parallelism can be used to solve text-critical problems and restore the text to a more pristine, original form.
For a more detailed analysis of the evidence and critique of contrary possibilities, as well as further discussion on the remaining simpler problems in the text of Deuteronomy 32:35-37, see my paper "A Text-Critical Analysis of Deuteronomy 32:35-37."