Can you upgrade the pentium chip in a gateway pentium 3

To answer your question yes you can upgrade an old Intel® Pentium® III processor to any processor within that family and socket http://ark.intel.com/ProductCollection.aspx?familyID=590&MarketSegment=DT. The real problem is going to be finding a processor that would be an upgrade (just so you know they are all been discontinued for close to 9 years now I think).
Comparatively speaking even the low end new computer today would be a great deal more powerful than anything that you could upgrade to within the Intel Pentium III line.

Christian Wood
Intel Enthusiast Team
 
Not to be mean
but
unless you get the PIII chip for free
then dont do it
Pentium III towers are so obsolete that
they are given away for practically free

If you are in USA or have Craiglist available then buying a $100 used tower
would blow the Pentium III away

the absolute cheapest new tower would be 100 times more powerful

Just not worth investing any money in, sorry :)