There seems to have once been a pronunciation of "accessory" with the main accent on the first syllable, and no stress on the second syllable. Many polysyllabic words ending in "-ary" or "-ory" put the main accent two syllables before this ending (as in "commentary" or "inventory"). But some of these words have come to have the main accent on the first syllable before "-ary" or "-ory", and "accessory" is currently pronounced everywhere with this accentuation (as far as I can tell).
The Oxford English Dictionary says
N.E.D. (1884) also gives the pronunciation (æ·ksėsəri) /ˈæksɪsərɪ/.
Walker's Critical Pronunciation Dictionary (1791) only gives a single pronunciation, with the main accent on the first syllable. It is a prescriptive dictionary, but Walker usually noted when he was proposing a new pronunciation, and he doesn't say anything like that in this entry.
It's also mentioned in Correct Pronunciation, A Manual Containing Two Thousand Common Words that are Frequently Mis-pronounced, and Eight Hundred Proper Names, with Practical Exercises, by Julian Willis Abernethy (1912)—as an incorrect pronunciation. (According to the preface, Abernathy intended to recommend only "the best current usage"). Abernathy cites "Worcester", which I guess would be J E Worcester, as the main "authority" he felt supported the pronunciation with the main accent on the first syllable. I don't know if the pronunciation was even common in Abernathy's time (making it one of the words he thought were "frequently mispronounced"), or if he just mentioned it because he had encountered it in some old dictionaries, and he wanted to advise people against using a pronunciation that he thought was outdated.
I don't know the distribution of this pronunciation in present-day English, or whether it represents a retention of the old accentuation pattern or an innovation based on some other tendencies (e.g. a general tendency to place the main accent on the first syllable of words, or analogy from the accentuation of "access"). I can't recall ever hearing it myself.
Possible stress on the first syllable when the second syllable is accented
Some of the comments beneath this question bring up a slightly different point. An English word can only have one main accented syllable (which is always a stressed syllable, and is often said to have the "primary stress"), but according to many analyses, there may be stressed syllables in a word other than the main accented syllable. (I found a document that seems to give a more complete explanation of English stress and accent, if you want to learn more about that: "Sentential Prominence in English", by Carlos Gussenhoven.)
The vowel in the initial syllable of "accessory" is reduced to something like /ə/ for many speakers, but not all.
It may be that some speakers have the main accent on the second syllable, but also stress the first syllable, and consequently pronounce it as /æk/ with an unreduced vowel.
Or, it could be that to speakers who reduce the vowel, a pronunciation with unreduced /æ/ just sounds like it has some stress on the first syllable. There are arguments about what "stress" is in English, and where it occurs. (E.g. not everyone distinguishes "accent" from "stress" the way I've tried to do in this answer.)
Words that are derived from other words with a different accentuation pattern can sometimes have adjacent stressed syllables like this; I would say that another possible example of this is "activity", related to the adjective "active", and pronounced with unreduced /æ/ in the first syllable even though the second syllable of "activity" has the main accent.
I found a source that calls this "tertiary stress" ("Word Stress – Part 1", p 111), but in any case there is no consensus as far as I know about the names for different "levels" of stress in English. Probably the least controversial way of describing the difference between the pronunciations is by referring to the presence or absence of vowel reduction.
