The mumbling, run on, ramblings of one under the influence of, opiates (Heroin, OxyCodone, Demerol), barbituates (Seconal, Placidyl, Tuinal) and some psychotropics (Valium, Xanax, 4Bar), manner of speaking while "On the nod".
From the words
"Chiva" -street term for Heroin and the suffix
"ese" -in the manner or language of.
"The strange utterance coming from your wife is actually Chivanese" the priest told the man, "So she needs rehab, not an exorcism."