Two stresses? I'm still not sure how your examples sound like
Nope. I've used the symbol " ' " to represent a syllable break. :D
The stress is on the second syllable [ka]/[kae]:
The first syllable houses a lax vowel, as in the sound of the "i" vowel in the word sit.
ChI'ka'go (pronunication #1) "Ch" is pronounced as [sh]
Note: The lax vowel syllable is closed by an unaspirated [h].
ChI[h]'ka'go "Ch" is pronounced as [sh]
For some speakers, [h] is omitted, leaving the lax vowel in an open syllable at a syllable boundary. In such cases, the following consonant is dragged across the syllable boundary to close the preceeding syllable,
ChIk'ka'go (pronunciation #2) "Ch" is pronounced as [sh]
For some speakers, syllable-final lax vowels are often reduced to schwa (i.e. the vowel sound in the), and schwa is often omitted syllable-finally,
Ch'ka'go (pronunciation #3) "Ch" is pronounced as [sh]
For some speakers, although rare, the lax vowel changes to a non-lax vowel. That is lax "I" becomes [i], as in see,