We have egfp1 promoter-less plasmid. 3 days post-transfection, the cells expressed GFP. We digested the plasmid to confirm the map. We found that everything is OK.
I did sometimes observe fluorescent protein expression from promoter-less plasmids (even ATG-less in some cases). However the expression levels were always extremely low and cell-type dependent. In virtue that different cell types can use different promoters, it is possible that your promoterless plasmid carries a DNA sequence upstream the eGFP which makes totally sense as a promoter for your target cell line. However in my experience this never led to very high expression levels.
Other possibilities are:
1) Your plasmid is not really promoterless (Sanger sequencing with a reverse primer on the eGFP should reveal the upstream sequence and solve the mistery)
2) Your plasmid has been annotated as promoterless but it contains one instead (annotate the plain text sequence of your plasmid using SnapGene viewer (free) or BLAST the upstream sequence to the nucleotide collection and human/mouse genomes)
3) The promoterless plasmid has been created by destroying a pre-existing promoter using restriction sites, but keeping essential components which your cells can still read. (BLAST also in this case to check for the most similar constructs).
4) As Reza was suggesting, eGFP might come from a contamination with a different cell line, or also a different vector. Check that your cell line is not expressing eGFP before transfection and that your plasmid mix is pure and not giving you strange or faint bands when digesting with restriction enzymes (you might have a contamination with another plasmid, especially if you are also working with other eGFP expressing vectors).
In addition to the answer from Francesco Aulicino, I'll add a 3.5 clause: there could be remnant elements like Kozak sequence that also allow the ORF to be transcribed. And since you're transfecting (I'll assume chemical, like Genejuice or Fugene?), there will be a vast number of plasmids (pDNA) per cell. Even if only a few of those are randomly transcribed, that should be enough to synthesize some GFP.