Chula is Mexican slang for a pretty, charming woman, close to "gorgeous" or "cutie" in English.
In the line "Y te prometo serte fiel, chula, tú eres mi vicio" (And I promise to be faithful to you, gorgeous, you are my addiction), the singer uses it as a pet name for his girlfriend. Its everyday sense is "cute" or "nice", as in qué chulo (how cool), but as a pet name it is a staple of Mexican regional music.
"Tu Y Yo" (You and I) is a straight-up love song, full of sweet promises. He brings flowers and asks for "un besito" (a little kiss), and promises "serte fiel" (to be faithful to you). He calls her "chula", Mexican slang for cutie or gorgeous, and "mi vicio" (my vice), meaning he is hooked on her.
The chorus is the dream life: "tú y yo viajando por el mundo entero, felices, gastando dinero" (you and me traveling the whole world, happy, spending money). The line that sticks is "Contigo quiero hacerme viejo" (I want to grow old with you), a lovely phrase to learn since hacerse viejo literally means "to make oneself old". There is also a Valentine's Day line that goes a bit further than flowers, which is a bit much for a first date. Listen for the shout-outs: "la Gemeliza" is the twins' name for their crew, and "La C, el 2 y el 4" spells out Calle 24, the act they are singing with. It closes in English: "You and me forever."