The name Iichiko (いいちこ) originates from the Ōita dialect and means “good” (いい, ii). Adding ~chiko (ちこ) is a way to lend emphasis to a word. It is thought that ~chiko may be a contraction of ~cha (ちゃ) and ~kon (こん). Iichiko is used more often to turn something down or refuse something than to evaluate it positively, a duality of meaning similar to kekkō des’ (結構です) and ii des’ (いいです) which can mean both “yes, please” or “no, thanks”. So, brush up your mind-reading skills before coming to Japan.
“Would you like something to drink?”
“Iichiko.”
“Um . . .”
“Iichiko.”
“Eh . . . Was that a yes-iichiko or a no-iichiko?”
“Neither. I want to drink Iichiko.”
“Ah.”
From Wiki:
母「ひろしちゃん、今日はさーみなっき、こん上着を着ちいきない（標準語: ひろしちゃん、今日は寒くなるから、この上着を着ていきなさい）」
Mother: Hiroshi-chan, kyō-wa samī nakki, kon uwagi-o kichiikinai. (Standard Japanese: Hiroshi-chan, kyō-wa samukunaru kara, kono uwagi wo kiteikinasai.)
Meaning: Hiroshi-chan, it’s going to get cold today, so wear this jacket.
ひろし「いいちゃ。今日は、ずっとぬっかろうけん（標準語: いいよ。今日は、ずっと暖いだろうから）」
Hiroshi: Iicha. Kyō-wa zutto nukkarō-ken. (Standard Japanese: Iiyo. Kyō-wa zutto attakai darō kara.)
Meaning: That’s okay. It’ll probably be warm all day.
母「風邪（かじぃ）引いたらつまらんき、着ちいきないちゃ（標準語: 風邪を引いたら困るから、着ていきなさいよ）」
Mother: Kajii hiitara tsumaranki, kichikinaicha. (Standard Japanese: Kaze-o hittara komarukara, kiteikinasai.)
Meaning: Wear it. If you catch a cold, you’ll have a hard time of it.
ひろし「いいちゃ（標準語: いいよ＝要らないよ）」
Hiroshi: Iicha. (Standard: iiyo = iranaiyo)
Meaning: I’m fine (= I don’t need it.)
母「着ていきないちこ（標準語: 着ていきなさいってば！）」
Mother: Keteikinaichiko (Standard: kiteikinasaitteba!)
Meaning: I said, wear it!
ひろし「いいちこ（標準語: いいってんだよ!＝要らないってば！）」
Hiroshi: Iichiko (Standard: iittendayo = Iranaitteba!)
Meaning: I said I’m fine! (I said I don’t need it!)