In this chapter, Samuel is born.
The story in this chapter should sound vaguely familiar. Hannah, like many other figures in the OT, is barren. Before this, we read about the barrenness of Sarah (Gen 17-18), Rebekah (Gen 25), Rachel (Gen 29-30) and Manoah's wife, the mother of Samson (Judges 13). In two of these cases (Sarah and Manoah's wife), the birth of their son was foretold by an angel. In the case of Rebekah and Rachel, this did not happen.
In fact, this is even more similar to the case of Rachel because in that episode, Jacob loved Rachel, and the LORD "opened [Leah's] womb" because he "saw that Leah was unloved". Rachel remained barren for some years, until the "LORD remembered" her in Gen 30:22. Here in 1st Samuel (what I will typically refer to as 1 Samuel), there seems to be a similar conflict between Hannah and Peninnah. Elkanah loves Hannah more and favors her, but Peninnah has children while Hannah is barren.
Hannah, just like Rachel, is destined to give birth to a son. Just like Rachel, it is a real battle for her, however. Rachel gave birth to Joseph, who turned into a heroic figure for his brothers and father, saving them from a famine. Hannah will also give birth to a heroic figure, the eponymous Samuel, but only after bitter tears and prayer.
To me, this chapter is a reminder of why polygamy doesn't work. We saw Rachel and Leah in conflict for years, with Leah feeling unloved and Rachel feeling like a failure for her barrenness. In this chapter, we see Peninnah provoking and harassing Hannah for years, and Elkanah is about as useless as Jacob (compare Gen 30:2 with 1 Samuel 1:8).
Eli is similarly clueless, unable to distinguish prayer from drunkenness. As an aside, this makes me wonder if it was a common thing for drunkards to wander into the tabernacle (presumably the courtyard, as the holy place is inaccessible to non-priests). I mean, is this something that Eli is used to, such that he expected it of Hannah as well? Remember the context; we are still living in the Judges period, when "every man did what was right in his own eyes".
The birth of Samuel is not predicted by an angel (nor was the birth of Joseph), but Eli blessed Hannah and "the LORD remembered her", just like he remembered Rachel. Like Samson, Samuel is devoted to the LORD as a Nazirite when Hannah swears that "a razor shall never come on his head". What is perhaps even more interesting is that Hannah brings Samuel to live before the LORD for the rest of his life, even though he is an Ephraimite. Remember that service to the LORD is considered the "inheritance" of the Levites. So I'm very curious what kind of form Samuel's service will take. Will he be informally inducted as a Levite, or is he just brought in as a servant to Eli and the priests? If I had to guess, I would suspect that Samuel is not permitted to serve inside the Tabernacle. It seems contrary to the Law that he would be allowed to do so, and yet later chapters in this book suggest he does just that.
Partly, I think we can ascribe this to the craziness of the Judges era, but it's also clear that the LORD favors and supports Samuel in his ministry (this will become evident in later chapters), even though Samuel is not a Levite and doesn't have a position under the Law of Moses to minister before the LORD. This is one of the paradoxes of the OT, where God seems to be supporting something that runs contrary to the letter of the Law. To me, this points to a higher law, like what is expressed in the ten commandments. If you love the LORD, have no other gods before him, and live in his service, it seems that other parts of the Law are more ... flexible? I'm not sure exactly how to express this concept, but I think Samuel's service is definitely a paradox of some kind, and it shows that the Law of Moses is not immutable, even in the eyes of the LORD. I don't know what I'm trying to say, other than that it is very interesting. I wonder how it should be properly interpreted.
On a minor note, Elkanah and his family are traveling to the Tabernacle is Shiloh to observe the three annual feasts that were laid out in the Law. Even through this chaotic period in Israel's history, we can see that at least some of the people are observing the commandments.