What's the difference between chance and fate to an epicurean? Do Epicureans believe in chance? I know they don't believe in fate.
Whether they espouse it or not, they believe in the slings and arrows of fortune. You cultivate friendships and peace because you are getting buffetted from outside forces. Over which you cannot control...
"Over which you cannot control..." UNLESS you develop friendships, and you take other precautions, to reduce the possibility of them occurring. If you do take steps, then you do reduce the likelihood of some problems. That is exactly how a prudent person acts, to take into our hands those things that are possible to control.
There's no "fate" by which gods or outside intelligent forces have complete control of the universe. There is an effective "determinism" however in certain non-living aspects of the universe, according to the letter to Herodotus (see below). This effective determinism in the way some things work does not however mean that intelligent animals don't have "free will" within certain limits, because we observe that they do, and we ascribe the cause of this to the swerve in the atoms from which the spirit is made.
As to "chance" there's also no god or outside intelligent force rolling dice. There is, however, the swerve, and the main way we see the swerve manifest itself in real life is that intelligent animals have a degree of free will,and are therefore unpredictable.
If you're a particle physicist then you can also discuss swerving at that level, but in the everyday world around us most things we see are the result of natural forces which can or could be predictable if we had enough understanding of all the variables involved.
Or at least that is my understanding of the texts.
Ref - Letter to Herodotus: "Hence, where we find phenomena invariably recurring, the invariability of the recurrence must be ascribed to the original interception and conglomeration of atoms whereby the world was formed."
Lucretius Book 2: "I desire you would attend closely upon this subject, and observe that bodies when they are carried downward through the void in a straight line, do at some time or other, but at no fixed and determinate time, and in some parts of the void likewise, but not in any one certain and determinate place of it, decline a little from the direct line by their own strength and power; so nevertheless, that the direct motion can be said to be changed the least that can be imagined.
 If the seeds did not decline in their descent, they would all fall downwards through the empty void, like drops of rain; there would be no blow, no stroke given by the seeds overtaking one another, and by consequence Nature could never have produced any thing.
 Besides, were all motion of the seeds uniform, and in a straight line, did one succeed another in an exact and regular order, did not the seeds, by their declining, occasion certain motions, as a sort of principle, to break the bonds of fate, and prevent a necessity of acting, and exclude a fixed an eternal succession of causes, which destroy all liberty, whence comes that free will, whence comes it, I say, so sensibly observed in all creatures of the world who act as they please, wholly rescued from the power of fate and necessity? That will by which we are moved which way soever our inclination leads us? We likewise forbear to move, not at any particular time, nor at any certain place, but when and here our mind pleases; and without doubt, the will is the principle that determines these motions, and from whence all motion is conveyed to the limbs. Don't you observe, when the barriers of the lists are thrown open of a sudden, the eager desire of the horses cannot start to the race with that celerity as their mind requires? Because the spirits, or particles of matter that maintain the course, must be got together from all parts of the body, and stirred through every limb, and fitly united, that they may readily follow the eager desire of the mind. You see then the beginning of motion rises in the heart, proceeds then by means of the will, and is thence diffused through every limb over the whole body.