Since your query specifies a civilised species, rather than a species possessing intelligence, awareness, soul, imagination and the like, I'd posit that such species already exist.
Or are very close to it.
A civilised species should have, according to human definition, a highly developed society or culture; refinement in taste and manners; or evidence of moral and intellectual advancement: humane, reasonable, ethical. I'd argue that humans are pretty consistent with the first definition, okay with the second and rather spottier with the third.
A random sampling of "hallmarks of civilisation" reveals certain characteristics:
- Advanced Cities
- Organized Central Government
- Complex Religions
- Job Specialization
- Social Classes
- Writing
- Art and Architecture
- Public Works
Let me introduce you to the humble termite! Already (and for millions of years), termites have built advanced cities containing housing, gardens, central air conditioning, roadways & public infrastructure. They have an organised central government of the strict monarchical model. They have job specialisation and a social caste system. Their cities are wonders of architecture and design that younger species are beginning to learn from.
We do not understand their communications or their minds, so we can't say for certain about things like art and religion and writing. Clearly, even without these elements, two of which even uncivilised humans possess, termites are actually pretty civilised.
For a look into what fully civilised termites might be like, I'd suggest The Termite Queen.