In Greek mythology, Chrysothemis ("golden law") is a daughter of Agamemnon and Clytemnestra — the one daughter-name shared by Homer's and Apollodorus's incompatible catalogues. In Sophocles' Electra she is Electra's cautious sister: she mourns their father yet urges accommodation with Clytemnestra and Aegisthus. Distinct from other Chrysothemises (Carmanor's daughter, a Danaid, a Hesperid).
Adapted from Wikipedia, "Chrysothemis" and "Electra (Sophocles play)" · CC BY-SA 4.0
I.Homeric and Apollodoran lists
In Iliad 9 Agamemnon offers Achilles marriage to whichever of his three daughters he chooses, naming Chrysothemis first, then Laodice and Iphianassa. Apollodorus keeps Chrysothemis but pairs her with Electra and Iphigenia instead. The shared name does not prove that Homer's Laodice is Electra or Iphianassa Iphigenia.
She belongs to the Pelopid house at Mycenae as sister of Orestes and (in tragedy) Electra — a stable genealogical anchor amid disputed sister-names.
II.Sophocles' Electra
Sophocles stages Chrysothemis as foil to Electra: she brings grave offerings for Agamemnon on Clytemnestra's orders, warns that continued public mourning will bring imprisonment, and later reports seeing Orestes's tributes at the tomb — news Electra at first rejects. She mourns their father but argues they lack power to avenge him openly.
The atlas id chrysothemis is Agamemnon's daughter. Other mythic Chrysothemises (Pythian hymn-singer, Danaid, Hesperid) are not this node.