彼らは私を長い事待たせた。

English Translation

They made me wait for a LONG time.

Is the particle に not needed between 長い事 and 待たせた?(or, perhaps this is just an informal quotation?)

@ericaw
You cannot insert any particle after 長いこと. Never. 長いこと (or 長い間) is an adverb. What you are trying to do is like transforming an adverb “beautifully” in English into “beauti-at-fully” (i.e. inserting a preposition “at” into an awkward position and making the adverb broken).

By the way, the standard spelling of ながいこと should be 長いこと, not 長い事. こと here functions as a kind of suffix, and it doesn’t mean “the thing/matter” any more. In this case, the Ministry of Education standardized the spellings in Hiragana.

We have another adverb with 長 and particle に: 長きに. 長き (ながき) is a written formal form of “adjective”. To use 長き as an “adverb”, you need に. For example,

田中長きに亘り、この町に貢献した。(たなかしはながきにわたり、このまちにこうけんした) = Mr. Tanaka contributed to this town for years.

If you want to make it more casual, it would be

田中さん長いこと、この町に貢献した。