According to just a few sources, Klytemnestra was married and had a child before she married Agamemnon. As one might expect, the story is not a happy one and includes many of the themes from the unhappy marriage between the two, including husband-killing and child-murder.
The most famous accounts of this come from the 12th Century CE Chiliades by John Tzetzes and the Epitome of Apollodorus (both of which are available on Perseus or in translation on Theoi.com).
“The nurse took Agamemnon with Menelaos
To Polypheides who ruled Sikyon
and who sent them in turn to Aitolian Oeneus.
Not much later Tyndareus brought them back again
and they drove Thysetes away to live in Cytheria
after he fled to the altar of Hera and they took an oath from him.
They both became sons-in-law to Tyndareus:
Agamemnon made Klytemnestra his wife
after he killed her husband, Thyestes’ son Tantalos
along with their new-born child. And Menelaos married Helen.”
τὸν δ᾽ Ἀγαμέμνονα τροφὸς μετὰ τοῦ Μενελάου
ἄγει πρὸς Πολυφείδεα, κρατοῦντα Σικυῶνος,
ὃς πάλιν τούτους πέπομφε πρὸς Αἰτωλὸν Οἰνέα.
μετ᾽ οὐ πολὺ Τυνδάρεως τούτους κατάγει πάλιν,
οἳ τὸν Θυέστην μὲν αὐτὸν Ἥρας βωμῷ φυγόντα
ὁρκώσαντες διώκουσιν οἰκεῖν τὴν Κυθηρίαν.
οἱ δὲ Τυνδάρεω γαμβροὶ γίνονται θυγατράσιν,
ὁ Ἀγαμέμνων μὲν λαβὼν σύνευνον Κλυταιμνήστραν,
κτείνας αὐτῆς τὸν σύζυγον Τάνταλον τὸν Θυέστου
σὺν τέκνῳ πάνυ νεογνῷ, Μενέλαος Ἑλένην.
“Agamemnon ruled as king of the Mycenaeans and married Tyndareus’ daughter Klytemnestra—but first he killed her husband, Tantalos, the son of Thyestes, with their child. They had a son Orestes and daughters Chrysothemus, Elektra and Iphigenia. Menelaos married Helen and ruled Sparta after Tyndareus gave him the kingship.”
Ἀγαμέμνων δὲ βασιλεύει Μυκηναίων καὶ γαμεῖ Τυνδάρεω θυγατέρα Κλυταιμνήστραν, τὸν πρότερον αὐτῆς ἄνδρα Τάνταλον Θυέστου σὺν τῷ παιδὶ κτείνας, καὶ γίνεται αὐτῷ παῖς μὲν Ὀρέστης, θυγατέρες δὲ Χρυσόθεμις Ἠλέκτρα Ἰφιγένεια. Μενέλαος δὲ Ἑλένην γαμεῖ καὶ βασιλεύει Σπάρτης, Τυνδάρεω τὴν βασιλείαν δόντος αὐτῷ.
There’s little to ‘confirm’ this story apart from a few mentions in Pausanias:
“I cannot say with precision whether Aigisthus began the wrongdoing or whether it was preceded by Agamemnon’s murder of Thyestes’ son Tantalos. For they say that he lived with Klytemnestra when she was a virgin, receiving her from Tyndareus. I don’t want to say that these men were wicked by nature….”
ὕστερον δὲ οὐκ ἔχω σαφὲς εἰπεῖν πότερον ἀδικίας ἦρξεν Αἴγισθος ἢ προϋπῆρξεν ᾿Αγαμέμνονι φόνος Ταντάλου τοῦ Θυέστου· συνοικεῖν δέ φασιν αὐτὸν Κλυταιμνήστρᾳ παρθένῳ παρὰ Τυνδάρεω λαβόντα. ἐγὼ δὲ καταγνῶναι μὲν οὐκ ἐθέλω φύσει σφᾶς γενέσθαι κακούς· –
“Others maintain that the bones of Tantalos are in this bronze container. This would be Tantalus the son of Thyestes or Broteas—for both stories are common—who lived with Klytemnestra before Agamemnon. I won’t deny that this Tantalos is buried there. I know that the other Tantalos, the son of Zeus and Plouto, has his tomb in Sipylos because I saw it and it is worth seeing.”
ἑτέροις δέ ἐστιν εἰρημένον ὀστᾶ ἐν τῷ χαλκείῳ κεῖσθαι Ταντάλου. τὸν μὲν δὴ Θυέστου παῖδα ἢ Βροτέου—λέγεται γὰρ ἀμφότερα—, ὃς Κλυται-μνήστρᾳ πρότερον ἢ ᾿Αγαμέμνων συνῴκησε, τοῦτον μὲν <τὸν> Τάνταλον οὐ διοίσομαι ταφῆναι ταύτῃ· τοῦ δὲ λεγομένου Διός τε εἶναι καὶ Πλουτοῦς ἰδὼν οἶδα ἐν Σιπύλῳ τάφον θέας ἄξιον.