On the sly

On the sly
 

I think one term is a la chita callando.
I would like to know if this phrase is international, and if there are other ways of saying this.

"A la chita callando" is unknown to me. I think "a hurtadillas" may be a good translation.

It's good in Spain.

It's used in Mexico too.
"Disimuladamente" could be a way of saying it more neutrally.

Agree with Robin, (for Spain)
A la chita callando. = En secreto o sin llamar la atención.
"A escondidas" or "a hurtadillas" is probably the most "universal" or like Angelica says, "disimuladamente" "con disimulo [y astucia]" "sigilosa y sutilmente"...

I believe "a hurtadillas" is a bit more literary than "a escondidas".

Also,
furtivamente, clandestinamente, de forma sibilina, a escondidas, de estranjis... por detrás de la cortina, callandito, callando, a cencerros tapados, confidencialmente, bajo cuerda, o por debajo de cuerda, encubiertamente, escondidamente, a escondidas, de matute [bootleg]... etc.
These are a bunch of synonyms that could be used with different connotations... one could start a thread for each, if you wanted, to see all the different nuances... but they all share the same basic idea. :)